Difference in playing a matched AI and choosing an AI

There seems to be two ways to play against AI. One is the practice against a matched AI where you choose races and based on performance the game sets the difficulty level. If you you loose to much the AI becomes lower.

Then there is custom games where you can choose your own AI.

Are these the same AIs? Will they use the same algorithms based on their level? Also, do the more difficult AIs cheat?

The AI's are always the same, unless you are playing in the Arcade where people can mess with the AI scripts.

There are many algorithms that AI can use based on level, not all opponents will play the same, even if they are the same difficulty. For example, one Terran opponent might go heavier bio and one might go heavier mech builds.

No, the AI does not cheat, they can not mine more minerals or build faster than you can, for example. The only thing they can do that might be considered cheating is control multiple units at nearly the same time.