The answer of above question depends by how do you define “one model”.
Should we count BMW 3-Series as one model?
Should we count each body type (compact, saloon, touring, coupe, cabrio)?
Should we count each engine version (318i, 320i, 325i, 330i, 335i, 316d, 318d, 320d, 325d, 330d, 335d, M3, in case of 3-Series E90)?
Should BMW M3 or BMW 3-Series Gran Turismo be counted as submodels of 3-Series or as separate models?
The answer according my PERSONAL classification
Volkswagen Group is 1 manufacturer, selling cars under 8 makes: Audi, Bentley, Bugatti, Lamborghini, Porsche, Seat, Skoda, Volkswagen.
BMW 3-Series is 1 nameplate.
Car Nameplates List have over 3,000 nameplates sold all over the world, 1945-present. Cars that are technically identical but sold under different names are counted separately, example Fiat Bravo / Brava or Mitsubishi Pajero (continental Europe) / Shogun (UK) / Montero (USA).
BMW 3-Series nameplate produced 7 successive models: E21, E30, E36, E46, E90-93, F30-33, G20.
Car Models List have over 5,000 models (generations) sold all over the world of which over 2,500 sold in Europe, 1945-present. Cars that are technically identical are counted only once here, Pajero / Shogun / Montero, but there are 4 generations of them.
BMW 3-Series was sold with up to 5 body styles: compact, saloon, touring, coupe, cabrio (in case of E36 and E46).
Car Models Database have over 3,500 body styles of the 2,000+ models sold in Europe, 1945-present (and actually there are more body styles, because in case of old cars if I do not know dimensions for each body style, I ignored them).
BMW 3-Series E90-93, each body style is sold with up to 12 engine versions: 318i, 320i, 325i, 330i, 335i, 316d, 318d, 320d, 325d, 330d, 335d, M3, some of them sold in rear wheel drive and all wheel drive options.
Car Models & Engines Database have over 20,000 combinations of body style, engine, drivetrain of the 2,000+ models sold in Europe 1975-present. This is the biggest database I compiled myself, manual data entry from AutoKatalog magazines issued yearly in Germany, which due to limited space of a printed book, they choose to not show separate row for manual / automatic transmission or trims / editions / equipment levels.
Larger than this are the databases made via scraping from various websites (as opposite of manual data entry).
Each engine version of BMW 3-Series F30-33 is sold with few trims / editions: (base), Modern Line, Luxury Line, M Sportpaket.
German Car Database made via scraping from www.adac.de have over 100,000 rows including every possible variation, 1975-present. United Kingdom Car Database made via scraping from www.parkers.co.uk have over 80,000 rows 1985-present.
They make so many rows that most customers refuse to purchase the over-detailed German and UK car databases and choose instead the Car Models & Engines Database, for example the car parts shops that do not need multiple rows for each engine.
Some customers thinks that a database with more rows is more complete, this is WRONG. Completion level is inverse proportional to detail level. The most comprehensive are the Car Models List and Car Nameplates List, because the more detailed ones cover cars sold in a specific continent only.
German Car Database although it have 5 times more rows than European Car Models & Engines Database, it is missing cars that are not sold in Germany, for example some Dacia, some Lada, all Moskwitch, all Zastava and other cars specific to Eastern Europe.
How many car models are sold in United States
Americans do not make distinction between multiple generations of same model, but due to government regulations of car market, each year is counted as separate model, manufacturers releasing each “2019 Model” during 2018. Also models sold here are offered with a smaller range of engines, for example in case of BMW 3-Series E90-93, only 4 engines are sold in US (328i, 335i, 335d, M3) compared with 12 sold in Europe.
Year-Make-Model-Trim-Specs have over 1,000 model nameplates, over 8,000 model years, over 50,000 trims, sold in United States 1990-present. Each year add about 2,500-3,000 new trims.
How many car models are sold in Australia
Australia government most likely do not regulate each year to be counted as separate model but websites such as Redbook.com.au shows each calendar year separately.
Australian Car Database have over 90,000 trims 1960-present. Each year add about 4,000 new trims.