Actually lenders can pull whatever they want, other than the mortgage universe where 99.99% of the mortgages in the US are underwritten on an explicit set of FICO scores.
Excepting that one case, the older scores are mostly used by CU's, dealer auto lending has wrapped their arms around the FICO 8 Auto and maybe starting to adopt FICO 9 AU in some cases, credit cards are mostly FICO 8, some FICO 9 now, and a few using the Bankcard industry option.
As stated elsewhere if you want to get basically all of your FICO scores that are currently in use, myFICO's service is the only game in town; that said, I personally just use Experians and then spot check my EQ/TU every so often, but everyone has different needs.
There's also single point in time 1B and 3B reports from myFICO which give all the scores once rather than a subscription.
I searched all forums, but couldn't locate a list of which FICO scores are used for which type of credit worthiness assessment. IOW, I recently discovered a FICO score used by auto loan companies. I know the FICO 8 score is used primarily to determine credit card approvals. I found a FICO 2 I think it was that is used for auto loans. My FICO 2 was acutely lower than my FICO 8 scores. I'd like a reliable resource for understanding all the various scores and I think that might be myfico, but I can't find it here. If it's here, please send a link. Thanks...
There is no simple answer to your question. Different lenders use different scoring models. Mortgage lenders almost always use EX FICO 2, TU FICO 4, and EQ FICO 5. But other than that, it's all over the place.