From what I understand of medieval armor, the governing factor tended to be more, “what can you afford?” Not, “well, I need to wear light armor because I’m agile.” Even full plate allows a great deal of mobility. Being able to stand there and soak off the blows has never really been an effective approach to armor. A combatant that can’t get out of the way of a charging horse, or is incapable of pulling themselves off the ground is dead. At that point, the expense of their armor and training is wasted.
The costs involved also applied to outfitting troops. Archers weren’t likely to be given much (if any) armor, because they wouldn’t come under direct attack. Disposable infantry might not be equipped much better. Knights would get the best their lords could reasonably provide because they were a serious investment, and needed to be protected (to a degree).
I’m inclined to blame Tolkien and D&D for the cloth wearing wizards, leather clad rogues and rangers, and the chain and plate soldiers. It’s entirely possible there are prior examples. There is some logic to it, too, ignoring wizards for the moment.
Hunters living off the land would have access to leather, and could convert that into clothing which, if properly treated, would last much longer than fabric clothes. Note, I said leather clothing, not armor. If they wanted to make armor, they could do that with the leather they found from their kills, but, if they chose to do that would probably depend on what wildlife they had to deal with.
For thieves and assassins, plate or chain doesn’t make a lot of sense, simply because of the noise it will invariably make. But, at the same time, leather armor is an iffy expense, simply because any armor can make some noise, and can cause you to stand out from the general population (which can be fatal). If your character is some kind of commando in a fantasy setting (it would be anachronistic, but for the moment that doesn’t matter), leather might not be a bad choice. It would make less noise than heavy armor, while still providing some protection, if not much.
For heavy combatants, plate and chain made sense (sometimes), if they could get it. Unfortunately, actually obtaining the stuff was an expensive prospect. For someone who worked as a mercenary, the best armor they could get their hands on might be leather or chain.
In cases where someone had access to whatever armor they wanted, the decision of what armor to wear had more to do with what someone was expecting to face, and what they would have to do, not their approach to combat.
Armor was very uncomfortable for traveling long distances, this is still true. So even if someone had plate, they’d probably not want to wear it while wandering.
Leather made sense for the vikings. Because they were
frequently exposed to sea spray, which is corrosive to most metals. In
general this also made plate and chain less appealing for sailors.
So, yes, there are specific roles for armor, but it’s not about agility or tanking (which doesn’t really exist outside of MMOs). (The real world equivalent to MMO style tanks are skirmishers or pickets, which are deployed to screen incoming attackers, and keep them off the artillery, archers, or support forces.) It is about who you are, what you’re doing, and where you’re going to be fighting; not the kind of a fighter you are.
I’ll also throw in this link to a good armor glossary with helpful terminology.