If I understand your question you want to put FTM on your laptop. FTM will load on your laptop like any other computer, and you can easily transfer you database to the laptop. I have FTM on my laptop so I can take my database any where I go regardless of internet availability.
I believe that the license is that only one copy of an FTM version can be in use at one time. I have never tried to install it on my Desktop for the reason I stated above.
Having the same database on two different computers presents problems of syncing the two files. I suspect it could be done with a program like Syncback, but you could only use one at a time, and then the most recent would be copied to the other computer.
It is also my understanding that the same program is contained within all flavors of FTM. the difference is what is packaged with them.