Yes. The myFICO products give you a lot of different scores. You are probably thinking of the FICO 8 Standard (Classic) score, which is the score the MF monitoring service is constantly giving you updates on. MF also gives other FICO 8 scores (FICO 8 Auto, FICO 8 Bankcard) as well as FICO scores from models that were used before FICO 8.
Chase gives you the FICO 8 Standard score and draws on the Experian data. American Express also gives the same score using the same data. Discover uses the same score but different data (TransUnion) -- same for Barclays. Citibank uses Equifax but the model is FICO 8 Bankcard Enhanced. This isn't a good match to the standard score for people who have extremely high scores, since the BE score goes up to 900 and Standard goes up to 850 -- but for ordinary people it's likely does a fair job.
Here's a link you might find helpful (though I don't know how up to date it is):
http://www.doctorofcredit.com/free-fico-scores/
