Ratcatchers: Especially in an urban campaign, this term is chosen specifically to disrespect and belittle adventurers. It comes from a more literal place, people who catch and dispose of rats and other vermin. It implies that adventuring is dirty work, unprofitable, undeserving of praise or respect.
Mercenaries: This one is more matter-of-fact. It’s still not a respectful term by any means, but there is a sort of professionalism to it. It also implies greed, that the PCs aren’t willing to do anything without the promise of pay. Also, there is the assumption that they are going to choose the violent solution to any problem, unless
Mercs: You might think this would be the same as mercenaries, but there is a wholly different intent behind the shortened version. This term assumes that the PCs are aggressive, that they only solve problems with violence. Not only that, this term implies that the violence isn’t just a means to an end, but something they actually enjoy.
Rogues: Not in the same context as the class. This is used to describe people who are likable despite their lawlessness. There is an implied charisma or charm, but also the assumption of greed as primary motivation.
Scoundrels: Like rogues in almost all ways, but without the requirement of likability. Still charm and charisma, just often more sleazy than actually likable.
Madcaps: Again, similar to rogue, but with a heavy implication of madness. Villagers who live near a haunted forest might call adventurers who go in there “madcaps.”
Bounders: Like scoundrels, but even without an implied charm. These are people without any sense of honor, motivated purely by greed.
Fixers: This one is straightforward. It doesn’t actively disrespect the PCs, but it also doesn’t elevate them above others. They are simply here to fix a problem, and after the problem is fixed, they’re useless.
Dungeoneers: This one is certainly more specific. It is similar to mercenaries, in that it doesn’t carry any respect, but it does have a professional air. Unlike mercenaries, there is an implied intelligence; a dungeoneer is an expert at dungeon-crawling. There isn’t as much of an emphasis on violence, instead there is an implied sneakiness. However, there is still an implication that greed is the primary motivator.
Explorers: This term may not be used for most PCs, but when it does apply, it is used in a respectful manner. It assumes even more intelligence, and it implies a scholarly bent, that the PCs are motivated by knowledge, not greed.
Wanderers: Like explorers, but without motivation.
Vagabonds: Like wanderers, but with the implication of being problematic to the community. Or, a sort of wandering scoundrel.
Pathfinders: Like explorers, but with the implication that they are clearing the way for the spread of civilization. There is an honor to this word, but also more implication of risk or danger.
Adventurers: There is more of an air of respect in this. The use of the word “adventure” implies a sort of storybookishness, there’s less of an implication of dirt and greed.
Heroes: This is a word chosen specifically to praise the PCs. It implies selflessness, a need to help others, and a certain level of competence.
Champions: Heroes, but tied to a specific place or group. The pinnacle of a community.
(I made this because it gets boring listening to NPCs saying the word “adventurers” all the time.)
Keep in mind that disposing of a threat the NPC in question had never seen or heard about will earn you zero glory. I mean, you’re an exterminator, right? There’s some gross pest and you slog around in the mud looking for it and clonk it over the head or whatever so respectable folks don’t have to look at it?
If you display wealth, you probably get the same kind of initial reaction as some petty asshole lordling. They want to convince you to spend money here, but you are a violent person who does not follow the social conventions of polite society so most of all they’re hoping you leave quickly and without breaking things or assaulting people.
Bringing a wizard along and letting people know about them probably changes things dramatically. Unless you’re in an extremely well educated setting, magic is mysterious and terrifying. They probably won’t try to burn you at the stake or anything, but even the peasants who are most grateful for magic happening because their lands are defended by a great wizard or whatever would probably prefer that this magic happens way over there. So you’ll likely get a lot of deference, some curiosity, but mostly a lot of poorly disguised fear.
Holy types are a big exception to most rules. If the locals recognize the symbol of your cleric/paladin’s god, then suddenly you go from a weird unknown to somebody they pretty much recognize and know what to expect from. They’ll treat the holy man like the appropriate type of clergy, and probably treat the rest of you as his/her retainers. If the god in question is not viewed favorably here, you will be seriously distrusted and hindered in a hundred subtle ways (and maybe a few overt ones). If the god is well loved, you’re honored guests.