Was playing around and I think I might have found a way to copy over the following:
Field name, field type & options (if multi-select), and field data
In my existing table that I want to paste into, I scrolled all the way over to the right and created a dummy field that was just named a, type single line text.
I went to the table I'm copying from, and copied multiple pieces of field data from 5-6 columns. I only clicked on the data from a record, not the whole column and the field name.
I then clicked over to the final table, and put my cursor in the dummy field (a) *and* in a new record, so one line below any of the existing data. After ctrl-V, the data, field name, and field types all showed up, to my surprise.
Hope this might help other folks searching for the same answer!
Edited to say: The field types did not include any formulas, lookup, etc. I'm guessing these would not copy over well, but the multi-select options, numbers with formatting, text fields, dates, all worked for me.
