Each credit bureau commissions its own FICO score formula, and each one seems to be a bit different from the other two.
Additionally, most of us have slight variances on our credit reports --an account that only reports on Experian, another that's clean on TransUnion but has some old lates on the other two, 3 inquiries on Equifax (EQ), 4 on Experian (EX), 1 on TransUnion (TU), and so forth.
So the combo of different score formulas and different credit reports means that more than likely, you wind up with three different FICO scores.
To make it crazier, TU is dragging its feet in providing the newer version of its FICO score, called (informally) TU04. All we can get here is TU98, and for some people the two scores are quite different. The EQ FICO here is the Beacon 5.0, which most of the industry uses, including your CU apparently. Good job showing them the report and score and getting an informal thumbs up! I love credit unions for that sort of thing. Meanwhile, Experian took all its marbles several years ago and refuses to sell consumers our own EX FICO score, preferring to flog its FAKO's instead. For a while, a number of us were able to join PSECU, a Pennsylvania credit union, but recently the member organizations refused new memberships from out-of-staters, so for most of us, our EX FICO's are mysteries.
It's perfectly fine to start with the CU card. Somewhere before you're six months out from your refi, you might try for a second card from a bank, so that you have two lines working for you, but don't apply any closer to refi time than that. As a rule, you shouldn't get new credit within a year of applying for a mortgage, but if you have to improve your credit profile, that's different. Nevertheless, don't go bat-wild and go on an app frenzy, loading up with a bunch of junky cards. Two are fine; three can be better when you have open installment loans, but it's not the end of the world.
Sounds like you have some good help from your CU. They're generally pretty wonderful folks.
eta: mortgage apps pull all three FICO scores, and they go with the middle score, which is why all that above is relevant. Refi's might not, but they probably will. The myFICO people are apparently working on getting TU04 here. If they succeed, you'll know two of your FICO's, and as long as the lower one of those two is acceptable, your middle score of the three will be at least that high. In other words, if your unknown EX score is lower than the lower known score, it won't matter, because they'll go with the middle score. If your unknown EX score is higher than your lower known score, then your middle score will be that number or the higher one from here, so you're in even better shape. I hope that makes sense. It always makes me a bit cross-eyed to type it out. 
There are lots of credit scores. And then there are your FICO scores.
There's a brisk industry in selling "credit scores" to consumers who (understandably) don't realize that the scores are worthless, in that they're used by very few, if any, lenders. These are the ones that we call "FAKO's", pun intended.
Many people have tried to track their FAKO's in hopes that they might sorta mirror their FICO's, but since they're based on different score formulas, they can go up when your FICO's go down, and vice versa.
I love credit monitoring services for the ability to track changes on your credit reports. But many of them come with FAKO's, and I had to learn to ignore the FAKO scores.
In addition, following the advice that comes along with FAKO scores can actually hurt your FICO's. 
So it's important to know how to separate out all this junk.
And the only reason that this is important is because it's much more likely that a lender is looking at your FICO scores. If someone doesn't anticipate needing credit (ever, ever again), then all this is meaningless. But at some point, most of us are going to have to deal with our numbers, for a mortgage, a car loan, whatever, so I prefer to know the score that my lender will be looking at. Which is why I'm not-so-patiently waiting for TU04 to come along.