Obviously this depends on your own lore, but my default lore-view would be:
Golems are similar to (but not quite) earth elementals.
Their creation is different - whereas elementals are spirits representing or personifying certain elements, with the power to manipulate that elements, that give themselves form by manipulating that element around themselves; golems are created beings (created by humans or other entities), and can't manipulate the element it is composed from. They can be composed from clay, earth, stone, wood, iron, flesh, or whatever... but the distinction is that golems aren't spirits with elemental affinity inhabiting and manipulating the matter, they are the matter, enchanted to give artificial life, and can't themselves manipulate the matter (anymore than say, throwing chunks of themselves). Their creator originally manipulates the matter to give them form, but they can't normally manipulate the matter themselves. And normally, they aren't very intelligent beings, being simple forms of limited human-created intelligence and technically barely even alive.
They aren't summoned into existence, or called forth like spirits; they are material gathered together from the environment and enchanted to give life, in the same way a magic carpet might be enchanted or a sword or animating and ""bringing to life"" a stone statue, suit of armor, or a wooden chair.
Now, depending on the magic used, you might take an existing spirit and bind it to a suit of armor or a human-shaped hunk of clay or a sword. That entity would then be intelligent, because the spirit bound is the actual entity and the spirit was already intelligent even before being bound. You could take a dog and cram a human's living spirit or a ghost/dead-human's spirit or a djinn, cramming that into a dog's body.
A spirit also could, of it's own will, inhabit a statue or suit of armor - it doesn't have to be something done to it by a third party - but usually without the proper bindings, the inhabitation is only temporary and a fairly weak bond. It's a weaker bond because it takes continued effort to sustain and continue animating the object, whereas being bound to the object makes you part of the object and requiring zero effort or sustained energy to remain within it.
Picture a skeleton. Now imagine that the spirit of the person who died is still floating around nearby. That spirit might re-animate the skeleton, providing a weak and fragile and temporary occupation, and the spirit eventually drains itself of energy trying to continue to animate the skeleton.
Picture a skeleton. Now picture a necromancer binding the dead spirit back into the skeleton. It takes an upfront cost for the necromancer to do this, but once down, the spirit will remain within the skeleton and the skeleton can be easily moved with minimal energy drain from the spirit itself. It doesn't have to be the original spirit of that skeleton that the necromancer binds - it could be a dog's spirit, or some other kind of spirit. But the original spirit probably has a more natural affinity for it, so it might adapt to it better, giving a greater chance of long-term survival.
Picture a skeleton. Now picture the necromancer instead of binding the spirit to the skeleton, using energy to animate the skeleton directly, without any spirit involved. This is closer to what a golem is. An inanimate object being manually animated by magic without spirits being involved. Except, now we take it a step further. The necromancer may easily bind dozens of skeletons and let them operate semi-independently from him, with minimal input. But if he has to manually animate skeletons, that takes alot of mental focus. It'd be hard to manually animate more than one at a time. Three or four if you have alot of practice at it. So golems go a step further - not only is the golem artificially animated, but the magi-user instead of binding an existing spirit, creates a kind of artificial spirit purely from magic and binds that to the golem.
I've never heard of a skeleton being used as a body for an artificial life, but I can't think of any reason why not. It's probably just that anytime you have a skeleton nearby, you probably already have a decent supply of non-artificial spirits to use anyway.
Also, I was using the term 'necromancer' because of the example of using existing spirits of the dead to bind back into skeletons. Golems themselves, being entirely artificial, is more enchanting and doesn't actually involve necromancy unless you put your artificial life into a dead body...
Because it's not a real life form, but something a wizard is creating, the intelligence is very simple and rough-around the edges. The artificial spirit then does the animating of the golem, requiring no mental concentration from the wizard. But because normal spirits themselves are life-forms, they have energy they can use to animate things. These artificially created lifeforms don't have energy in themselves, so they need some way of either A) gathering energy from the environment (requiring a greater skill of the creator when creating the artificial life), or more commonly B) precollected energy is stored either nearby.
If the energy is stored in a fixed location, that limits the geographical range of the golem. This still makes them useful for, say, guarding an area, but it means if they leave the range of the energy source they crumble and fall apart (depending on the material) and the artificial life fades out ("dies") from lack of energy.
More commonly, the energy is pre-collected by the wizard and stored inside the body of the golem (in some object within them or perhaps directly in their material), so the golem carries the energy source around with it's body. Eventually it'll use it up, but if the golem was created skillfully enough, and if it isn't very active or is dormant for long periods of time, it might last decades or even a few centuries.
A third option is the wizard having the golems use energy from the wizard's own body. If the wizard lacks skill in gathering and storing energy in other objects (like crystals or metals), existing lifeforms already naturally produce and store energy quite efficiently. It probably would give some wizards an ego trip that they are literally sustaining another life form, artificial and simple-minded though that lifeform may be. It also prevents other wizards from taking control of your golems and using them against you, because you can easily cut off access to their energy source (yourself). It suffers from the same mobility limitation of not having an internal energy source, but at least it's still semi-mobile in that you can travel and they can travel with you, and probably have a decent rage (maybe even a few miles, depending on your skill in creating them as well as depending on terrain interference) around you.
Uh, and in answer to what 'category' they would be in would depend on your other categories. By what characteristics are you categorizing all your beings? Golems fall into the 'created' category. They also have different element categories depending on the material used to create them. They are melee, if categorizing by attack type...
The thing about categories is that they only make sense in contrast to what's not in the category. I'm a human. I'm also American. I'm also male. I also like cake. I have brown hair. What category you put me in depends on what categories are available. If you are categorizing by 'Cake Fan' vs 'Not cake fan', then I'd go in the 'Cake fan' category. But in someone else's categorizations, I'd go in the 'Programmer' category (as opposed to 'Composer' category), but I might also fit slightly under the 'Artist' category or 'Designer' category at the same time. It's even been proven mathematically possible for something to fit into two mutually exclusive categories at the same time (with upset and messed up a whole generation worth of math concepts back around the end of the 19th century).
