In most fRPGs, a zombie is indisputably undead and normally - at least within the standard game rules - a product of deliberate use of evil magic or theurgy. Oddly, it's usually fairly high powered magic as well, which is at odds with the the zombie's general role as a low level antagonist. Other sources of zombies (such as bad places) may exist, but these are generally not covered in the rules. Depending on your fRPG of choice, this may or may not be an issue.
In the matter of other zombie characteristics, the fantasy zombie is usually slow moving, mindless, non-contagious1 and not hungry2 (but frequently mindlessly aggressive). Against that, they are immune to headshots a la Romero, but require no special measures other than applied violence to destroy them (and usually violence short of complete dismemberment as well). The magic of animation is generally thought to preserve them from decay (in some systems, perhaps because the "negative energy" which drives them deters or kills detritovores that would otherwise break them down).
As noted, the fantasy zombie is usually created as a puppet, but seems to end up as a mindless speed bump for low level characters … how all these zombies end up unattended is a subject of frequent speculation, but a common theory is that, given that many fRPGs assign a fixed limit to the number of undead that a given caster can control at any one time, any units that aren't actively controlled become "roamers" unless properly contained (although some systems allow undead to be left with "standing orders" that they will obey until further notice).
Of course, variations exist - fRPG zombies may be hungry (but good luck distracting them with your iron rations), may move faster or may require complete dismemberment to destroy (which usually just equates to a lot more hit points and/or some rules for severed body parts fighting on alone). There may also be 'customised' versions with specific magical effects added to spice up a monster that would otherwise be a bit routine for the PCs.
In a very few cases, there may be sentient - or at least semi-sentient - zombies floating about. These are more likely to be revenant material, but may be just a variant class of zombie. This may or may not make a difference in the rules.
Game and Story Use
- It's all down to the genre you play - and what genre your PCs are savvy in.
- As undead that are typically created and controlled you may need to decide whether ontological inertia applies to them or not - do they all drop dead again when you kill their creator, or do they just become an uncontrolled menace?
- Long term, fantasy zombies are mostly likely to rot down to skeletons.