As a quick and dirty explanation,
Slashing weapons like axes and swords typically work best against soft targets. Things like unarmored monsters and animals. Humanoids too if they aren't wearing anything better than leather. Although excessively large monsters and creatures will reduce their effectiveness depending on the size of your weapon. A Two handed sword for example is better against a giant than a short sword.
They typically cause the most harm by severing limbs and causing massive bleeding, they can also hit major organs without too much trouble. Their downsides are a general lack of applied force, spreading the force from the blow over too large an area. And same materiel armor tends to not have much trouble deflecting the strikes.
Piercing weapons like spears pikes and the stab attack of a halberd are typically better at damaging through armor and attempting lucky organ shots, while maintaining some of the bleed effect of a sword or axe. A good quality spear made of the same or better materiel as your opponent's armor can basically make the armor pointless, as the force focused on the small point of piercing weapon overwhelms the armor's ability to resist it, unless it is a particularly crappy spear. You won't puncture an iron helmet with a wooden spear for example.
Like the slashing weapons they can cause bleeding, and they also tend to apply more force than a slashing weapon, allowing more broken bones, and armor or skull puncturing. They aren't likely to sever limbs though. And although many people claim they are better for organ hits, I seem to get more of them with a sword than a spear, so your mileage may vary. (In pre-materiel rewrite versions they always had a built in better chance to hit organs.)
Bludgeoning weapons are the big heavy things like a hammer, maul, or mace. Unlike the other weapons heavier is always better. While steel is great for cutting weapons, steel is almost garbage for bludgeoning weapons. Silver is ideal, iron is functional, adamantine is like a styrofoam bat. They are also good against armor like a spear, as most if not all armor is only designed to resist cutting in the game, not bashing.
They typically cause broken bones and compound fractures, and very little bleeding, only causing light bleeding as the result of a compound fracture. Also compound fracture wounds are very difficult if not impossible to clean, leading to a high chance of infection. They are the ideal weapon choice against non organic hard golem type creatures like iron men and bronze colossi, applying massive force, enough to break the body parts clean off by force alone. And a hammer to the head of any organic creature is likely instant death regardless of armor.
Bolts arrows and blowgun darts are like little mini spears, with much higher velocity and much smaller penetration sizes. They are small, and light so don't cause broken bones or organ hits as often as a real sword or spear can, but they tear through almost any armor, even stuff made of better materiel, like a hot knife through butter. Note that they are just as effective thrown as fired from their respective launchers.
I guess that wasn't as quick as I thought.