What is the difference between intention and intension? If one intends to do something is this intent part of the concept of intension?
The "intension" of a concept is its meaning, whereas the "extension" of the concept is the set of the things that fall under that concept. The most helpful way to see the distinction is with a pair of concepts that have the same extension, but different intensions.
For instance "renate" (="having kidneys") and "cordate" (="having a heart"). Everything that is the one is also the other, so the terms are coextensive. Yet there is still clearly a difference in meaning between them.
"Intentional" on the other hand in these contexts usually means "being about something". (The idea of doing something "intentionally" i.e. on purpose is actually quite different.) Mental states are often intentional, that is to say, usually we are seeing that p, or believing that p, or doubting that p, or whatever. There is some content p to the mental state that it is about.