In the main series Pokémon games, there are six main stats that a Pokémon can have (five stats in the Generation I games):
In Generation I (Red, Blue, and Yellow), the Sp. Atk and Sp. Def stats do not exist—instead, there is a single Special stat that counts as both offense and defense.
The stats that you see a Pokémon have in a game are actually calculated from several factors; the most important factor, the factor that varies by species, is the Pokémon’s Base Stats. Two different Marill will always have the same Base Stats, and these are different than the Base Stats that a Charmander has. These range from 1 to 255, with 255 being the absolute max possible (Blissey‘s base HP is the only obtainable Pokémon with a number this high).
There’s also Individual Values, also known as IVs (or just IV for a singular Individual Value stat). Every individual Pokémon, whether wild or hatched, have individually different IVs for each of their different stats, ranging from 0 to 31 (as of Generation III) for each stat. Two different Marill may have the same Base Stats, but they may have different in-game stats (shown on the stat screen), and that’s due to these two Marill having different Individual Values. In short, IVs are the random variance between Pokémon of the same species—that individuality.
Another important factor in the stat calculation is a metric commonly known in the community as Effort Values or EVs (or just EV for a singular Effort Value stat), although officially these are referred to as base points. Similar to IVs, every individual Pokémon can have a different amount of EVs for its stats—it can have a range from 0 to 252 (or 255 prior to Generation VI) for each stat. These start out at 0 for each stat, and by fighting wild or Trainer Pokémon (or by other methods that raise EVs, such as using vitamins, etc.), these can be raised and will increase the actual in-game stat accordingly. The sum of a Pokémon’s EVs cannot exceed 510 EVs—once it hits 510, that’s the limit, and it can earn the Effort Ribbon for reaching that point.
Nature is also a factor for the Pokémon’s in-game stats. There are 25 different Natures that a Pokémon can have, and 20 of them increase one stat by 10% while also decreasing one stat by 10%—5 Natures are considered neutral and neither raise nor lower a Pokémon’s stats.
Lastly, one incredibly important factor for Pokémon’s stats is actually a pretty obvious one: its level! The amounts that Base Stats, Individual Values, Effort Values, and Nature affect stats are generally relative to the Pokémon’s level, so, for example, a Pokémon at level 50 would receive roughly 50% of the benefit from Effort Values as it would at level 100. These don’t always work out to an exact 1:1 proportion, but generally speaking, you’ll find EVs and IVs at least to be around that. Level is an important factor in the formula, but it’s just that: a factor.
With all of that being said, the stats that you see on the screen of your game are not just some number pulled out of thin air—they’re a product of several different factors. That’s why you’ll almost exclusively see Base Stats used on websites and in online Pokédexes—it provides the base representation of a Pokémon’s strength in that stat and is easy to compare against other Pokémon’s Base Stats.