Can TCAS give an RA for one aircraft and a TA for another?
It's hard to give a definitive answer without more information.  My go-to for TCAS details is the FAA's Intro to TCAS II. In general, an RA will try to coordinate with the other aircraft, but such coordination doesn't require the other aircraft also issue an RA, it only listens for other RA "intent" messages and makes sure it doesn't issue a conflicting RA.

Here's some possibilities:


A marginal RA encounter.  Each airplane has slight differences in calculation , so, as the FAA manual linked above reads, "In a majority of the TCAS/TCAS encounters, the two aircraft will declare the other aircraft to be a threat at slightly different times"
The TCAS of one aircraft was set to TA-ONLY, although this normally only happens if the airspace is busy
One had an inaccurate pressure altimeter reading
Thresholds are larger at higher altitudes and this could have contributed to the higher altitude pilot receiving only a TA
One airplane was running TCAS I instead of TCAS II and couldn't get RA's.  This is probably not the case if the aircraft was commercial.
They're running different versions of TCAS with slightly different algorithms