Why is the credit score here different than what I see on my credit report? Does refinance (pulling my credit) take a hit on the score?

There are dozens of different “official“ credit scores.  FICO produces different scores using different models (“model 8 is most common these days) and even a single model score can be calculated three different ways using information from the three credit bureaus, which are often slightly different.  Turbo offers a TransUnion “Vantagescore” from the credit bureau TransUnion, which is similar to but not the same as a FICO score.  To see all of your different credit scores you would need to buy a subscription at one of the credit bureaus. I doubt it is worth it, the credit score is just a crude way of measuring your reliability as a potential borrower if you are applying for credit.

separately, “soft“ credit inquiries do not change your score, but “hard“ credit inquiries will temporarily lower your score. A hard inquiry happens when you apply for new credit even if you don’t get it.  Because applying for credit indicates that you need money, it may suggest to lenders that you are at a greater risk of being unable to repay it.