I feel like this depends a bit on what you consider to be "big differences", and what sort of abstraction library you have in mind.
So long as you're only concerned with placing and formatting characters on the screen, support for the subset of "extended VT100" which is required is essentially universal. There is no disagreement over what escape sequences can be used to move the cursor, for example, or to clear the screen. Using an abstraction layer like termcap is effectively a no-op here; it will output the exact same sequences for any modern terminal application.
And if you want to support modern and/or esoteric features like embedded graphics or custom characters ("sixels"), you're probably going to handcraft that anyway, as support for those features is very limited, and most abstraction libraries won't support them at all. So I'm not sure I see the case for an abstraction at either end of the spectrum.