How do store actually work?

It's a mix.

Gold coins (Apex coins) are the main currency; you have to purchase those or you get a few doing the battle pass over time.  Be careful with these.  When you buy something it does not give you a confirmation, it just takes the coins.  I accidently bought a skin I didn't want and I could not get a refund so you've been warned.

Red coins are basically useless.  I think you can use them for recolours (if you have the base skin) or boosting probability of loot ticks to have various cosmetic items you might have an interest in.  They can also be used for buying legends you have not unlocked yet.

Green coins I've not worked out as I'm not big into cosmetics.  I think there is a special store for those where you can use them for rare items.

Heirloom shards are the rarest of all.  You can use those for heirlooms for legends (typically melee weapons) or skins that evolve over time based on performance (damage).

Just poke around the store and be careful what you click on.  You'll figure it out.