Alison-

from what you've written, it could be that Stuart and Beth *only*

relate along the line of Stuart's paternal grandmother's maternal
line (x match).

It depends on which lines precisely the common surnames belong to, and
whether or not the surname match is coincidental (it happens often
enough, even when dealing with the same small town of origin). More
than one line of relatedness *could be possible*, but isn't demanded
by the information you've given.

Since one way (but necessarily all the ways) Stuart and Tim relate are
through the direct maternal line (for both of them), then, yes, at least
partially, Tom and Stuart relate in a different way than Stuart and Beth.
They could partly be related in the same way though, or at least partly
similar ancestry.

---
Tim, Stuart, and Beth all show as 3rd to 5th cousins to each other.

Stuart and Beth share two surnames (Stuart's male line) in common, as
well as the Ukraine for place of origin. Beth is an x-match to
Stuart's paternal grandmother, but not an x-match to Stuart. So is
she related to Stuart in more than one way?

Tim is an x-match to Stuart but not to Stuart's paternal grandmother.
So is Tim related to Stuart differently than Beth is? Or since she
might be related to Stuart in more than one way, Tim could be related
to Beth in one of the ways?

The chromosome browser shows Tim and Stuart overlapping, and Beth and
Stuart overlapping, with a few very small overlaps between all three.

Thank you,

Alison Greengard
Lakewood, Colorado, USA