To me roleplaying is just doing and saying things that you think your character would. It doesn't have to be in-depth, if you're playing a dwarf you don't have to be able to trace your family tree back 12 generations. You don't need to always speak in character or even have a backstory, you don't have to "act" to roleplay.
There are many times in D&d where you are simply roleplaying while interacting with other PCs or NPCs. Discussions with friends and allies, things that may have fairly high stakes like planning on how to invade the BBEG's lair but don't really have any immediate risk or reward, where there's not a lot of uncertainty. It's just freeplay.
But there is something derogatory about the term "rollplay" which is the point.
I don't know if there is an acceptable term anymore than there is for answering the question, "what is an acceptable term I could use to insult you?" I think that the solution isn't about finding the magic word that works; instead, the solution likely rests in framing your language in terms of your personal experiences: e.g., "my group and I had difficulty with roleplaying 4e skill challenges" rather than referring to skill challenges, combat, or whatever else as "rollplay." I would also be careful to avoiding insult generalizations that characterizes the play of others like "It seems that some people want rollplay to drive everything outside of combat instead of roleplay."
Then there are encounters. To me an encounter is when there's significant risk or reward at stake. You want to talk to a prisoner so you convince the recalcitrant jailor to see them, perhaps sneak past guards or find some other means. Then there may be issues with getting out.
That encounter can be as simple as talking to the jailor and convincing them somehow, perhaps you bribe them, make a promise, talk your way in. Some DMs will never call for a single roll, it all depends on what is said and how. In other cases the DM will try to roleplay the jailor and take their desires and needs into account then decide if what is said or the bribe offered is good enough to convince them. If it's uncertain, the DM calls for a roll.
Another way to handle it is for the DM to have predetermined appropriate skills and be open to others. There are consequences to rolls or expenditure of other resources. I do this sometimes for things like overcoming traps or purely physical challenges like getting over a mountain mentioned above. In my game the scenarios are resolved with rolls against a DC with the help of spells and magical items. Other games may have other resources such as reputation and expending influence points or a dice pool to draw from. In 4E of course they added the success and failure scorecard, something I personally dislike.
I would call the latter rollplay, just like I call combat rollplay. There is nothing wrong with it, it's a big part of my games. But if that's an objectionable term, I don't know what else to use. Mathematical resolution because you're comparing a number achieved to a target? Except that doesn't work because spells can bypass. Mechanical resolution? Rules based resolution? I'm assuming you'll consider non-roleplaying encounter just as bad?
There has to be some phrase to describe the different types of resolution out there that is not objectionable because the two ways of handling encounter resolution are fundamentally different.
