Many auto lenders use FICO 8 Auto Enhanced, but some use FICO 8 Classic. Also used are FICO 04 Auto Enhanced, FICO 98 Auto Enhanced, etc.
Virtually all mortgage lenders use the same combination of very old FICO models (much older than FICO 8). They will use FICO 04 for EQ and TU and FICO 98 for EX. They might well use other kinds of numbering or naming conventions for them (though the actual models will be the ones I just told you).. Fortunately, myFICO makes it easy to check your mortgage scores. They will be labeled as "mortgage scores" when you get your scores from myFICO.
When do you plan to buy a house? If you have the time, it's best to get all your credit cards except one reporting $0 with the remaining card reporting a small positive balance before you pull all those scores -- just because it costs money each time you pull them. (It costs money if you use myFICO, that is.) Getting your CC balances as I just indicated will give you a score boost. I can suggest some free tools that will enable you to assess what your CC balances are reporting at currently.