The two TA adapters are functionally different in terms of attachment:
a) The long available one for the SLC uses a seperate stud that attaches to the binocular, and then the adapter attaches to it, in contrast;
b) The new adapter for the NL fits directly into a socket on the just introduced NL x52 *
From the instruction sheets, TAs-NL vs TAs-SLC:
For some more images of the adapter for the SLC (including the collet fingers in the adapter that grasp the stud),
along with the 3rd party offering from Outdoorsman for the previous NL production, see:
Tripod stud for Swarovski NL
* As SuperDuty indicates, when the NL x52 and the adapter were announced, it was also stated that:
a) previous NL x42 and x32 production could be modified to accept the adapter, and;
b) ongoing NL x42 and x32 production would be adapter compatible.
Looking at the page for the NL adapter today, more information has been added:

See at:
TAs tripod adapter - SWAROVSKI OPTIK
John
p.s. Two images of the mounting socket on the NL x52:

Both cropped and adjusted:
L from:
The brand new Swarovski 14x52 NL Pure. Did the workhorse of binoculars for hunting just get better? // GOHUNT. The Hunting Company
R from:
NL Pure Stud