There’s precision, complexity, timing, punishment, and resource consumption.

With precision, you have to do things in a certain amount of space. To make something more difficult with precision, you shrink the spaces that the player has to fit through tighter. Think of having a smaller road with for a racing game, having a boss with bigger attack hitboxes so the player has less space to dodge to, or having a smaller keypress window in a rhythm game.

With timing, you have to do things in a certain time window. You make games more difficult timing-wise by shrinking the time window. Think shorter time frames for a race, faster attacks from a boss, or tighter keypress requirements in a rhythm game.

Precision and timing are closely tied to one another so they are often treated as the same thing. In Rhythm games, for example, they are near-inseparable.

With complexity, you have to do a certain number of things. you increase difficulty with complexity by increasing the number of things you have to do. Think More turns back-to-back on a racetrack, more unique attacks you need to memorize from a boss, or longer rhythm game courses.

With punishment, you have to do things while only failing a certain number of times. To increase difficulty with punishment, you shrink the number of times you can fail before losing. Think of racing games where your car degrades from collisions or where there’s cliffs on the track sides, where the boss attacks do more damage, or where you get fewer miss allowances in a rhythm game.

With resource consumption, you have to do things with access to a limited amount of time, energy, items, etc. to increase difficulty with resource consumption, you shrink the amount of resources available and/or how long resources last during use. Think giving a player less health, a boss more health so each attack is worth less, giving a player fewer health potions, make the player have to fight more enemies total (not necessarily more per fight).

All games shift difficulty with any number of these. a mechanics game will increase difficulty by demanding better precision and timing, increasing complexity, etc, usually a combination of all methods I mentioned. a numbers game will change difficulty almost exclusively by increasing resource consumption, usually by increasing enemy health pools and nothing else. It’s also common for difficulty to increase by just making good items more scarce.