Someone else asked this question in another Japanese learning space I'm in and I attempted to research it to find an answer for them, but I didn't quite get a conclusive answer.
On goo, they define 卓 as 物を置く台 and they define 台 as 物をのせるもの
I also found this article which I briefly skimmed through, and while it doesn't specifically address the difference between the two words/kanji in this question, there were mentions of them throughout, but it didn't seem like there was any clear difference, that I could find at least.
All I've been able to guess so far is that 台 is maybe broader in meaning in regard to tables than 卓, since 卓 is defined as a type of 台. I also noticed from my brief research that 卓 doesn't seem to be used by itself very often. All I was able to find was 卓を囲む when it came to that. Otherwise it was mostly just compounds like 食卓. Where as with 台 it seemed that it could be used by itself or in compounds, either way.
I am assuming that there is perhaps a way to distinguish between the two based on the characteristics of any given table at hand whether it would be more appropriate to refer to it as a 卓 or a 台, but I was not able to find anything covering this.
