I know about autoit and about autohotkey but I am not sure that they are the same. What other good automation programs are there? Should I use different programs for automatic browser mouse clicks and keyboard pressing?
A Google search with the keywords "browser test automation framework" will yield many links for you to check. These frameworks usually handle mouse clicks and keyboard pressing. I do not recommend using different software for automating mouse clicks than for automating keyboard pressing. If you believe you have special needs that would motivate doing so, you should alter your question to describe those needs.
You might want to check out TestApi at http://testapi.codeplex.com/
Also, automation frameworks emulate key presses or mouse clicks via messages directly to the OS which bypasses the keyboard and mouse hardware & drivers.
You might wish to investigate the freeware versions of iOpus iMacros.