Continuum of Roleplaying
Roleplaying can be a pretty broad term. Is a MMORPG roleplaying? Is Monopoly roleplaying?
You could spend a lot of time arguing what counts as roleplaying, but the answer is not yes or no, it's a matter of degree. Even “move your token” board games contain an iota of roleplaying. When you move the shoe on the Monopoly board, that shoe is your character, however minimal that character may be. If you identify with it, it's your character.
This is a stab at defining the complete spectrum of roleplaying, from barely having a character all the way to complete immersion. The order is not intended to indicate merit. You're not a better person if you're engaged in first degree roleplaying rather than second degree roleplaying. You're just roleplaying more, which could be appropriate or not depending on the game you're playing.
5th degree — You are not represented in the game even if you control events in it (third person, no representation). You have a god's eye view. You may control units but with the understanding that they serve you instead of representing you.
4th degree — You are represented by a token in the game, with no discernable personality or unique game stats (first person, token representation). You move your token but only minimally identify yourself with it.
3rd degree — You act as the character in the first person, but the nature of the character does not influence your decisions (first person, no decision alteration). You could be unaware of the rules of the game or just not taking them into account, or the character might not have unique stats. You might be ignoring the character's personality or the character might have no defined personality.
2nd degree — You make decisions based on the character's game statistics but not its personality (first person, rules conscious tactics). Again, you might be ignoring the character's personality or the character might have no defined personality.
1st degree — You take actions based on the personality of the character, including making decisions you know are unwise or poor tactically but which fit the character's knowledge or preferences (first person, personality roleplaying). Rules take a backseat to personality.
zero degree — You think you are the character. You are unaware that you are a player (first person, immersion). Not to be confused with someone who is just playing themselves, not a different character.
In tabletop roleplaying games we are mostly concerned with first through third degree roleplaying, but the fourth and fifth degrees reveal traces of roleplaying in other games. In a nation building computer game, you may have no in-game identity but you are still trying to be a good emperor and therefore literally playing a role (fifth degree). When you move your shoe around the Monopoly board it's “you” that lands on Boardwalk, not “my shoe” (fourth degree).
Second degree roleplaying (tactics) is where most computer MMORPGs hit, along with lots of other computer “RPGs” and not a few D&D games.
Is there a difference between someone who engages in first degree roleplaying (personality before rules) out of committment to their character versus someone who doesn't know or understand the rules? Maybe, but again it's not about merit.
Zero degree roleplaying doesn't happen in any game I know of, but I'm including it for perspective since it's the logical continuation of the spectrum. It's either the realm of virtual reality where the players don't know they are participating, or a player who has had a mental breakdown and can't distinguish reality.
Note that first through third degree roleplaying do not specify whether the player is making metagaming decisions to improve the game. A first degree roleplayer could make decisions true to the character which still hurt the game (slavish roleplaying). The druid who won't go into the city. The loner who can't imagine teaming up with the other players.