So a friend of mine is doing a Halloween one-shot in which we'll all be playing kids out for trick-or-treating, and all the magic/fantasy/etc is in our imagination, so things like our class etc are kind of based on what we're dressing up as for Halloween (e.g. my character is dressing up as Poison Ivy so she's going to be a druid). It's adorable. At any rate, I've also decided that my character is going to have a stuffed animal she carries around with her everywhere that she would imagine coming to life to help her out in combat, but I have no idea whether it would be more appropriate to classify it as a familiar or an animal companion, since mechanically I'm not sure if I detect a ton of difference between them? But I'm also having a really hard time finding specific answers! Could anyone provide a little guidance as to what kind of differences there would be between them in gameplay, and based on that maybe which would be more appropriate? Right now I'm sort of leaning towards familiar being more appropriate. (FWIW we'll all be third-level, if that makes a difference)

The spell or feature where it originate will indicate if the creature for you is a familiar or an animal companion as each come with different set of rules for how it can act or move under your control.

If it's an animal acting indenpendently under the DM control then it's neither of those.

If the goal is to have it fight, then you don’t want a familiar.

familiars cannot attack.

Ranger Companion, Druid Companion, or Sidekick would be your main choices.

A companion is subject to whatever rules grant that companion to the PC. For example, most of the time a companion is granted by the Beastmaster Ranger subclass. A familiar is subject to the rules that grant that familiar to the character, typically the find familiar spell.

Familiars can't attack, but they can still take the help action, deliver touch based spells, and be a target for the Dragon's Breath spell.