FICO releases a big new family of models every 3-6 years. Within the family there is a "classic" flavor and there is also flavors targeted toward specific industries: Auto Enhanced, Bankcard Enhanced, etc.
FICO 8 was released in 2008-2009. It includes the FICO 8 classic and the FICO 8 Auto Enhanced. Whether these are run on Equifax, Experian, or TransUnion data, they are still called by the same name.
Earlier models have more confusing and less consistent naming conventions. For example. FICO 04 was released in 2004, but Equifax calls it Equifax FICO 5, Experian calls it Experian FICO 3, and TransUnion calls it TransUnion FICO 4.
You wanted to know what most auto lenders are using nowadays. Mostly they are using FICO 8 Classic, FICO 8 Auto Enhanced, or FICO 04 Auto Enhanced. (But bear in mind that EX, TU, and EQ call FICO 04 version 3, 4, and 5 respectively.) A small number of lenders might use something else altogether: VantageScore 3.0, FICO 04 Classic, etc.
The FICO 04 family differs from the FICO 8 family in that each credit bureau has a different top range for its FICO 04 score. In FICO 8 all bureaus have exactly the same range.
The Classic flavor differs from the Auto Enhanced flavor in that the AE flavor has a higher top range than does the Classic. For example, FICO 8 AE has a top range of 900 whereas FICO 8 Classic has a top range of 850.
You also wanted to know a simple way to figure out exactly what score a particular lender might use for its auto loans. The simplest way is to ask them. You'll want to know three things:
What FICO version is it? (8 = FICO 8 and 3/4/5 = FICO 4)
What flavor is it? (Classic vs. Auto Enhanced)
What credit bureau will they be pulling their data on?
In theory the lender should know the answer, though a particular customer service rep may not know and it may take mutliple gentle/courteous calls to find the answer for sure.
But aside from asking, there's no simple way to predict what scores a particular lender might use.
