imo the difference doesn't mean much, the TS could easily pull a bar long long over a few thou..
I am not a fan of those test bars. That test (not using the TS) could be telling you the spindle bore is out or there is a microscopic bit of crude or a burr in the spindle nose
I would
1) make sure the test bar is a straight cylinder (plate, indicator and a V block....if its not straight you're beat before you start)
2) Rotate the test bar - do you get any run out, and is the run out the same at both ends? (probably not....why I don't like mounted test bars)
3) Do the test you just did, but as well as measuring at the HS and other end of it, rotate it 180 (as exact as you can, say using a pointer and gear on the out board side)
If the readings are identical, then then the test bar is truly aligned with the spindle in the plane. With a good chance it won't be,
knowing the difference, lets you determine if the issue is test bar to spindle error, or spindle to bed error. a has to be the same value b as per diagram below