What both terms convey to me is "a communicative act intended to instill a belief in the interlocutor".

To pick a recent example, if I say "Yesterday I felt faint while waiting in line", it's not clear how one is to tease apart what beliefs I intend you to have: it seems naive to suggest that because this looks superficially like a declarative sentence, all I intended was to convince you that I felt faint yesterday.

Depending on the context, I could be trying to convince you that I'm in poor health and in need of affective support, or (if you're my doctor) that I have a treatable issue, or that waiting in line is hazardous to one's health.

I agree that if we're having a debate, that sets up some context and expectations about my speech acts which are different from what they'd be if we were having a conversation, and different again from what they'd be if we were merely making small talk, which isn't quite the same as a conversation. And there are yet other modes of talking, such as gossiping, holding forth, and so on.

So I'm suspicious of assertions about "most communication" which do not attend to this variety of possible modes of communication.