A score is generated for a specific report. Lenders will see the score for the info on your report on the day that they pull it. If the information has not changed since you got your score from Equifax, then they will see the same score (our accounts are always aging so the information is always changing a little bit).
Your TU score works the same way, you are just only getting access to it once every quarter. It's accurate at that time, but if the information changes over the next month or so, and the lender pulls then, it very well could be different.
ETA: Also, the TU score you pull here is TU98. A lot of lenders are using a newer version of TU, TU04. So your TU score is actually probably not going to be the same as what a lender will see unless they are using the same version. People on here have reported differences between TU98 and TU04 ranging +-40 points or more.
The version of EQ you get here is the same version most lenders are using.
Starting Score: ~500 (12/01/2008) Current Score: EQ 681 (04/05/13); TU 98 728 (01/06/12), TU 08? 760 (provided by Barclay 1/2/14), TU 04 728 (lender pull 01/12/12); EX 742 (lender pull 01/12/12) Goal Score: 720