Pokemon cards with the same name and different features
According to Rulebook, page 22:

DECK BUILDING
(...)
Also, except for basic Energy, you can only have 4 cards with the same name in your deck. This means you can have only 4 cards called “Pignite” in your deck, even if they all have different attacks. Finally, your deck must have at least one Basic Pokémon in it.
(...)

You can see that deckbuilding rules does not talk about cards, but card names.
There are also some parts of Pokémon's name that do not count toward this rule, that is outlined in Rulebook on page 21:

WHAT DOES AND DOESN’T COUNT FOR A POKÉMON’S NAME?
• Some Pokémon cards have extra information after their name, such as a Level or a symbol like GL. A Pokémon’s name changes how you can evolve or play certain cards. Level is not part of a Pokémon’s name:
    ◆ Gengar, Gengar LV. 43, Gengar LV. 44, and Gengar LV.X all have the same name
• Symbols at the end of a Pokémon’s name are part of a Pokémon’s name:
    ◆ Alakazam, Alakazam 四, and Alakazam ☆ all have different names from each other
    ◆ However, δ (Delta Species) is not part of a Pokémon’s name. Aerodactyl and
Aerodactyl δ (Delta Species) have the same name
• An owner or form name in a Pokémon’s name is part of the Pokémon’s name:
    ◆ Meowth, Alolan Meowth, and Rocket’s Meowth have different names
When you are building a deck, you can have only 4 copies of a card with the same name in it, except for basic Energy cards. If your deck has 1 each of Gengar, Gengar LV. 43, Gengar LV. 44, and Gengar LV.X, you can’t put any more cards named Gengar in your deck! However, you could have 4 Meowth, 4 Alolan Meowth, and 4 Rocket’s Meowth.
When evolving, the “evolves from” Pokémon name must match the Pokémon being evolved. So Graveler can evolve from Geodude, or Geodude LV. 12, but not Brock’s Geodude.

There is no difference in casual or tournament play, if they follow official rules. There might be some formats that change those rules, like Prerelease tournament that diverges from official rules such as:

40 cards in deck
only 4 prizes
no &quot;only 4 Pokémon with the same name deck&quot; rule

I strongly recommend to play using the official rules at all times so you are not surprised when you attend a league or a tournament for the first time.