Due to the fact I'm constantly getting into arguments with Competitive Pokémon Players (which is something that I'd like to apologize for, BTW), I thought I should try to explain the some of the main differences between the battles I've been in, and the ones they have.

Seeing as how I haven't been in any Competitive Pokémon Battles myself, I may get certain things wrong, so bear with me.

Now, since it'll be much easier for me to explain what non-Competitive Pokémon Battles are, I'll start with them.

Non-Competitive Battles are those done anywhere outside of a Competition, and that don't require a Trainer Club Account (which I don't have, solely because of my control freak dad), and are generally pretty loose about rules and stuff, compared to Competitive Battles.

If I were to battle my sister here at home, via Local Wireless Communications, it would be a non-Competitive Battle.

If I were to Battle her over the Internet, it would STILL be a non-Competitive Battle.

If we were to both do Random Matchup Battles on Battle Spot, at the same time, and (by pure chance) wind up Battling each other, it would STILL be a non-Competitive Battle.

Non-Competitive Battles have simpler, more straightforward rules (the same ones used at places in-game like the Battle Subway or Battle Maision, typically), and go by what I refer to as the "2 Tier System": The Pokémon allowed at such places in-game; and the "Special Pokémon" (all of which are Legendary or Mythical) that aren't.
(And they either allow these Pokémon or they don't, depending upon the rules of the particular non-Competitive Battle in question.)

Non-Competitive Battles are typically referred to as "Casual Battles", and those who've only done such battles (like myself) are typically called "Casual Players".
(Being as Hardcore into Pokémon as I am, I prefer to say "non-Competitive Battles" and "non-Competitive Players, however, as I don't really consider my level of interest, knowledge, or experience with Pokémon as "casual".)

Competitive Battles (AFAIK) include the Rating Battles done on the Battle Spot (which require Trainer Club Membership), as well as RL and Online Competitions (such as the official VGC), and also battles that have special Competitive rules, and divide Pokémon into Tiers and such (Ubers, OU, UU, etc.), like those on Smogon.

The Rules, Tiers, and many other things constantly referenced in the Comments on my Pokémon Blogs, are referring to things that apply to Competitive Battles, which DON'T apply to non-Competitive Battles, such as the ones I described before.

These links can probably do a WAY better job of explaining what Competitive Battles are than I can, though:

https://smogon.com/dp/articles/intro_comp_pokemon

https://www.pokemon.com/us/strategy/making-the-jump-to-video-game-competitive-play/

https://ign.com/wikis/pokemon-sun-pokemon-moon/Beginner's_Guide_to_Competitive_Pokemon