what are the diff. types of functions?

By the sounds of it you're talking about events, not functions. Events are specific for each instance, you can refer to the wiki for a full list of events for any given instance.

Example:

local Brick = script.Parent

function omgPart_wuzTouched(part)
	print(part:GetFullName() .. " touched " .. Brick:GetFullName())
end

Brick.Touched:connect(omgPart_wuzTouched)

omgPart_wuzTouched <-- That's a function

print <-- That's a function

Touched <-- That's an event

connect <-- That's a method that connects a function to event so that when the event is fired the function 'omgPart_wuzTouched' is called