Some people think apoy and Red are the same. Even on something like Bulbapedia and Pokemon Wikia. Lol. But that is NOT true! In this, the comparisons will say the differences, and the similarities.

Game Debuts

Red
First appearance: Pokemon Red and Blue (GameBoy)

Fire
First appearance: Pokemon FireRed and LeafGreen (GBA)

Gym Battles

Red
It has been a long time since I read the Pokemon Manga, but I can remember Red did win most of the Badges in Kanto. If I remember correctly, Red appears in Pokemon Origins where he defeat all the Kanto gym leaders. Especially when Red's Charmander defeated Brock's Onix and Red's Charizard defeated Giovanni's Rhydon. Good one Red's Charizard.

Fire
apoy only appears in the third gen Pokemon games like Pokemon FireRed and LeafGreen and Pokemon Colosseum. So you'll have to play Pokemon FireRed and LeafGreen if you want to see apoy battling gym leaders. He also appears in Super Smash Bros Brawl though.

Character

Red
Red is a silent Trainer (As seen in HG/SS), in fact, he doesn't talk at all! Not much else is known about him, except he wanted to be the greatest Trainer. Also, in R/B, he only sagot yes or no to any questions. In HG/SS/Black 2/White 2, Red wears Fire's clothing instead of own clothing.

Fire
A Trainer with the same goal as Red, apoy was a stubborn Trainer in the beginning, but dedication to his goal paid off, with him entering the Indigo League as well as going to Sevii Islands and then own any of the 386 Pokemon like Hoenn Pokemon (like Blaziken). He is Red's video game counterpart and he first appeared in Pokemon FireRed and LeafGreen.

Pokemon

Red
Again, I haven't read the Pokemon Manga in a long time, so I don't remember all the Pokemon Red caught. But here are some:
Starter: Bulbasaur--Evolved into-->Ivysaur--Evolved into-->Venusaur
Gyarados (Given to him from Misty)
Nidoking
Pikachu
Poliwhirl--Evolved into-->Poliwrath
and some others.

In Pokemon Origins, Red has Charmander who is now a Charizard. He also owns Ratatta, Pidgey, Metapod, Spearow, Nidoran Male, Jolteon, Hitmonlee, Lapras and Victreebel. He also owns legendaries like Articuno and Mewtwo. He owns all 150 Kanto Pokemon like Pikachu.

Fire
He owns any of 386 Pokemon in Pokemon FireRed and LeafGreen since he is a Hoenn trainer, not a Kanto trainer despite he goes to Kanto instead of Hoenn. Pokemon FireRed and LeafGreen trainers like Pokemon FRLG rival are Hoenn trainers. That's why Pokemon FireRed and LeafGreen are Hoenn Pokemon games that takes place in Kanto instead of Hoenn despite Pokemon FireRed and LeafGreen are the remakes of Pokemon Red and Green because Pokemon FireRed and LeafGreen are NOT Kanto remakes. Let's ilipat on.

Also, the two have had some other differences that aren't above! Here are some more.

Red actually defeated Team Rocket in Kanto, but apoy also battled madami Team Rocket members in Sevii Islands that Red doesn't like Johto's Archer and Ariana.

apoy had caught a Shiny Pokemon in FRLG, Red hadn't since shinies introduced in G/S.

Fire's Charizard (As seen in Super Smash Bros. Brawl) actually does things! Unlike Red's Charizard, who appears in Pokemon Origins.

In addition, apoy appears in Super Smash Bros. Brawl where Sinnoh Pokemon like Palkia appear, Red doesn't. Which is why Pokemon FRLG along with RSE can migrate Pokemon to DPP alongside HGSS.

apoy has caught madami Pokemon than Red does during his FRLG appearance, and Red only use any of his 150 Pokemon in RBY like Squirtle wheras apoy uses any 386 Pokemon in FRLG like Chimecho.

Red appears in the 2013 anime, Pokemon Origins, apoy doesn't.

Red and apoy do both appear in Pokemon Generations though. Red and apoy appears in The Adventure and The Challenger respectively.

Also, Red appears in the manga, apoy doesn't.

Red is a Kanto trainer, apoy is a Hoenn trainer who goes to Kanto in Pokemon FRLG.

Because apoy owns madami Pokemon than Red does, Red only owns Kanto Pokemon like Pikachu while apoy owns 386 Pokemon like Tropius.

Red appears in all 8 bit Pokemon games (Red/Blue/Yellow/Gold/Silver/Crystal). Red is playable in RBY while he is an NPC in GSC. Red also appears in both Pokemon Stadium games, Pokemon HeartGold/SoulSilver and Pokemon Black 2/White 2. Red did not appear in FRLG which is why apoy replaced Red in FRLG.

Thus, apoy first appeared in Pokemon FireRed/LeafGreen. He also appeared in Pokemon Colosseum/Emerald/XD and SSBB (by the name of Pokemon Trainer who owns Ivysaur, Charizard and Squirtle).