Physalis of the Southeastern US:
Sullivan, Janet R. "The genus Physalis (Solanaceae) in the southeastern United States." Rhodora (2004): 305-326.
Sullivan, Janet R. "Nomenclatural innovations in North American Physalis (Solanaceae)." Rhodora 115.963 (2013): 290-292.
Sullivan, Janet R. "Systematics of the Physalis viscosa complex (Solanaceae)." Systematic botany (1985): 426-444.
Weakley, Alan S. 2022. Flora of the Southeastern US. UNC Chapel Hill, Chapel Hill, NC. Available at https://ncbg.unc.edu/research/publications/
Turner, Billie L., and Mahinda Martinez. "Systematic reassessment of the North American Physalis viscosa complex (Solanaceae)." Phytologia 93 (2011): 260-269.
Pretz, Chelsea, and Rocío Deanna. "Typifications and nomenclatural notes in Physalis (Solanaceae) from the United States." Taxon 69.1 (2020): 170-192.

Physalis of the other US regions:
Jepson eFlora. 2022. Physalis of California, decription, list, & links to online keys: https://ucjeps.berkeley.edu/eflora/eflora_display.php?tid=9696
MICHIGAN FLORA ONLINE. A. A. Reznicek, E. G. Voss, & B. S. Walters. February 2011. University of Michigan. Web. May 27, 2022. https://michiganflora.net/genus.aspx?id=Physalis.

Sullivan's "The genus Physalis (Solanaceae) in the southeastern United States" is available online at the Biodiversity Heritage Library (click here).

This species list encompasses the 20 species of Physalis (and Physa-likes) commonly found growing wild or cultivated in the following 14 states: Alabama, Arkansas, Delaware, Florida, Georgia, Kentucky, Louisiana, Maryland, Mississippi, North Carolina, South Carolina, Tennessee, Virginia, West Virginia.

Physalis alkekengi is now Alkekengi officinarum
Physalis angulata
Physalis angustifolia
Physalis arenicola
Physalis carpenteri is now Calliphysalis carpenteri
Physalis cinerascens
Physalis cordata
Physalis x elliottii (hybrids of Physalis angustifolia and P. walteri)
Physalis grisea
Physalis heterophylla
Physalis lanceolata
Physalis longifolia
Physalis macrosperma
Physalis missouriensis
Physalis mollis
Physalis peruviana (cultivated)
Physalis philadelphica
Physalis pubescens
Physalis pumila
Physalis virginiana
Physalis walteri

Very occasionally, a random individual of the annual Physalis acutifolia gets introduced from the Southwest and pops up in a heavily human-disturbed area, but they don't seem to persist.
The Neotropical annual Physalis lagascae is a rare weed of sugarcane fields in Mississippi and Louisiana.

Some quick lists of key traits and species groups:

ANNUALS (with taproots): Physalis acutifolia, Physalis angulata, Physalis cordata, Physalis grisea, Physalis lagascae, Physalis missouriensis, Physalis philadelphica, Physalis pubescens.

PERENNIALS (with rhizomes): Alkekengi officinarum, Physalis angustifolia, Physalis arenicola, Physalis cinerascens, Physalis x elliottii, Physalis heterophylla, Physalis lanceolata, Physalis longifolia, Physalis mollis, Physalis pumila, Physalis virginiana, Physalis walteri.

COLORFUL FRUITING CALYXES: Red-orange = Alkekengi officinarum. Tangerine-orange = Physalis angustifolia, Physalis x elliottii, or Physalis walteri.

SAND-LOVING SPECIES: Physalis arenicola mostly Floridian, occasional in sand of other coastal plain states. Physalis angustifolia beaches from Florida panhandle to Louisiana. Physalis x elliottii in peninsular Florida. Physalis lanceolata mostly sandhills of the Carolinas. Physalis macrosperma in Arkansas, Louisiana, Texas. Physalis walteri on east coast beaches or sand, Florida to Virginia.

Based on:
Sullivan, Janet R. 2004. "The genus Physalis (Solanaceae) in the southeastern United States." Rhodora: 305-326.

See also:
Pyne M, Orzell SL, Bridges EL, Poindexter D. 2019. Physalis macrosperma (Solanaceae). Journal of the Botanical Research Institute of Texas 13(1): 31-50.
Thieret, John W. 1971. Physalis lagascae (Solanaceae) in Louisiana: New to the conterminous United States. Sida, Contributions to Botany 4(3): 277-277.
Whitson, M. 2011. Proposal to conserve the name Physalis (Solanaceae) with a conserved type. Taxon 60(2): 608–609.
Whitson, M. 2012. "Calliphysalis (Solanaceae): A new genus from the southeastern USA." Rhodora 114(958): 133-147.

Physalis is basically a New World genus. Most species previously described from the Old World (for example, Alkekengi officinarum) have been segregated from Physalis after phylogenetic analyses suggested that they were genetically distinct from the New World species.

About 25 species of Physalis are native, naturalized, or widely cultivated in the US.

As a whole, the genus includes about 100 species, though new species are still being described, particularly from Mexico, which is the center of diversity. At least 65 species of Physalis are known to occur in Mexico.

The number of species found growing native or naturalized drops as you move down through Central and South America. For example, Flora Mesoamericana recognizes 26 species as occurring from southeastern Mexico through Central America. Flora of Argentina accepts 7 species as occurring in Argentina, and 10 when southern Brasil, Chile, Paraguay, and Uruguay are included.

Several species of Physalis are weeds now found worldwide in areas with warm climates. These include annuals such as P. angulata and P. pubescens, and perennials such as P. peruviana and P. viscosa.

REFERENCES FOR MEXICO:
Physalis in Jalisco: http://www.organicaeditores.mx/biblioteca.jsp?bookid=30
Martínez M, Vargas-Ponce O, Rodríguez A, Chiang F, Ocegueda S. 2017. Solanaceae family in Mexico. Botanical Sciences 95(1): 131-45.

Solanaceae in Mexico: Martínez et al. "Solanaceae Family in Mexico" at https://doi.org/10.17129/botsci.658

For southern Mexico and Central America:
Davidse, G., M. Sousa Sánchez, S. Knapp & F. Chiang Cabrera. 2030. Solanaceae a Caprifoliaceae. 5(1): ined. In C. Ulloa Ulloa, H. M. Hernández Macías, F. R. Barrie & S. Knapp Fl. Mesoamer. Missouri Botanical Garden, St. Louis.

SOUTH AMERICA:
Instituto de Botánica Darwinion. 2018. Flora del Cono Sur.

AUSTRALIA:
Physalis Fact Sheet from the Electronic Flora of South Australia: http://www.flora.sa.gov.au/efsa/lucid/Solanaceae/Solanaceae%20species/key/Australian%20Solanaceae%20species/Media/Html/Physalis.htm

REFERENCES FOR THE US:
Southeast: Sullivan, Janet R. "The genus Physalis (Solanaceae) in the southeastern United States." Rhodora (2004): 305-326.
New Mexico: Flora Neomexicana III : An Illustrated Identification Manual, part 2, 2nd edition, 2020.

Trichomes (aka hairs) are one of the most important ID features for Physalis. Their density, length, structure (simple/unbranched vs. branched; glandular vs. not) and orientation (antrorse/forward pointing, divergent/outward pointing, retrorse/backward pointing) are all crucial for species determination, in part because you can always see them regardless of whether the plant is fruiting or flowering.

Physalis heterophylla : Click to see full size. This species has long, dense, simple (unbranched) pubescence that is often glandular and has a divergent (sticking straight out) orientation. Photo © Clifton Albrecht from https://www.inaturalist.org/observations/112449559

Physalis cinerascens : Click to see full size. This species has short, dense, pubescence that is branched and non-glandular. Photo by Victor Engel from https://www.inaturalist.org/observations/33734991

Physalis longifolia : Click to see full size. This species has short, simple, non-glandular pubescence with an antrorse (forward-pointing) orientation. Photo © Wayne Longbottom from https://www.inaturalist.org/observations/87642880

Physalis virginiana : Click to see full size. This species has short, simple, non-glandular pubescence with retrorse (backward-pointing) orientation. Photo © jtuttle from https://www.inaturalist.org/observations/12170907

Perennial. Densely fuzzy with simple (unbranched), glandular, divergent (pointing outward) hairs.

One of the most common perennial species in the US, with one of the broadest ranges, from the eastern US across to the West.

Click for examples.

Click for rough range map.

Occurs in 30+ US states: Alabama, Arkansas, Colorado, Connecticut, Delaware, District of Columbia, (Florida)*, Georgia, Illinois, Indiana, Iowa, Kansas, Kentucky, Louisiana, New Jersey, New York, North Carolina, North Dakota, Ohio, Oklahoma, Oregon, Pennsylvania, Rhode Island, South Carolina, South Dakota, Tennessee, Texas, Vermont, Virginia, West Virginia, Wisconsin, Wyoming.
*May occur in north Florida/Panhandle, but would be rare. Does not occur further south in peninsular Florida.

Also occurs in southern Canada. Doesn't get into Mexico.