Hi Ryan,
If it was internally cached, the file size must be much larger just to give you an indicator.
If cached, the results will be the same, AFAIK; otherwise, we would have many posts here from render farm results and jumping frames.
Caching cloth, to my understanding, is point-based; there is no derivation.
If you would like to test this, write out an Alembic file and load it into the Cached file as a "reference." It is highly unlikely that both change in the same way.
Since it is easily imaginable that I do not have the two setups that cause your trouble, please get a second opinion on that, meaning get in touch with Maxon's tech support at
https://www.maxon.net/en/support-center
(It might take longer this week as we have a company-wide meeting.)
All the best