Indeed.

"Register": I immediately know what it means and it takes tenths of a second for me to make the decision to click (or not to).

"Sign up": despite having a CEFR C2 level of English and using it at work every day, I still need to think for a few seconds if this is a registration or a login (cf. "sign in").

For a native speaker I suppose the latter is (marginally?) easier, but for a non-native, it's much harder, not even close.

Your examples are very illustrative, but I would argue that both phrases suffer from being too generic. I wish that there wasn’t such a push for “one word” CTAs. Examples of alternatives I’d advocate for depending on context:

“Create an account”

“Subscribe to mailing list”

“Submit contest entry”