bta gave a very good reply. I just wanted to add on saying that the different methods are suspectible to different means of detection by the gaming company. Hacking into the game client via memory monitoring or packet analysis generally is more easily detectable. I generally don't recommend it since you can get caught very easily.
Screen-scraping used with input emulation is generally the safest way to bot a game and not get caught. Many people, (myself included) have been doing it for years with no problems.
In addition, to add an additional step between detecting what's going on in the game and providing input, some games require extensive calculation before you can decide what kind of input to provide to the game. For example, there was a game where I had to calculate the number of ships to send when attacking the enemy, and this was based on the number of ships I had, the type of ships, and who and what kind of enemy it was. The calculation is generally the "easy" part since you can do that usually in almost any programming language.