Adventurer is a title given to individuals whose occupation is, obviously, adventuring. "Adventuring" implies going on adventures, but in practice is more likely to involve murder, security detail, object and artifact retrieval, tomb desecration, and waking things best left sleeping. Adventurers usually have short lifespans, but make up for it by wielding phenomenal cosmic power and carrying around enough material wealth to destabilize the economies of entire regions. Usually Adventurers are also Player Characters. The inverse is even more common.
Broadly speaking, an adventurer's job description will fit into two categories, with some overlap. Both involve killing things, but one is slightly more social than the other.
Murderhobos is a term used (originally pejoratively, but occasionally affectionately) for the player characters in RPGs, both in video games and tabletop games. The term arises due to the fact that most adventuring characters and parties are technically homeless vagrants, generally living on the road and sometimes in temporary accommodation, and the default solution to problems faced by the typical adventurer boils down to killing things until the problem is solved or treasure is acquired. In many games (especially older pure hack and slash-types of the type that Gary Gygax despised) killing things and taking their stuff is simply the order of the day, all morally acceptable and proper, either because that's all the players are interested in doing or all the GM can come up with. In more nuanced settings, "Murderhobo(s)" is used especially to refer to characters (or entire parties) of looser morals who tend to regard massive collateral damage as an inevitable and unremarkable consequence of their actions, or who are quite happy to slaughter otherwise friendly NPCs at slight provocation or the prospect of financial gain (basically, munchkins).
Although it is a fantasy standard that adventuring parties are welcomed into towns and villages and hailed as saviors, there is a small trend for this to be inverted in some games and stories (usually for comedy's sake) and have the protagonists be treated as the homeless serial killers they actually are, either by having them rejected from civilized society or by having the NPCs/minor characters respond with pants-shitting fear whenever the heroes present themselves. Murderhobos left to their own devices are bad news for the region they occupy, so they are often dealt with by giving them quests that take them to dangerous places in distant locations, where they can kill some other monsters (or at least some foreigners).
Mercenaries are people who fight in conflicts for the sake of direct profit provided by their employer. In most fiction, they exist to provide a group of people who have military force capacity, while not being associated with particular political and societal factions. This means that most mercenaries are used for protagonists and anti-heroes, as it's much easier to create a believable and unique character without restricting them to a set group of beliefs of a faction. Equally frequently, the mercenaries are shown in the dark light as well, being pragmatic villains who have little of interest in anything besides money, thus allowing them to be the bad guys by doing anything and everything evil for the sake of wealth.
In many a games, the PCs are hired as mercenaries to provide services for someone, starting from removal of Giant Space Hamsters from a cellar of a local noble, to poisoning the kings during a banquet, so his brother's cousin sister can usurp the throne. And since the parties can range from Chaotic Stupid to Stupid Evil to Stupid Good (even at the same time), this means that all characters can act towards common goal, without having to resort to fratricide, because they can't agree on an approach to the situation (as most players use their status as mercenary as an excuse to do things out of characters, because "Derp, Money").
- See here for a man who fights like a murderous hobo.