I was wondering if I can hookup one computer to an other computer and download files from one to another even if they are not the same make and how I can do it?

Yes, you can do this and there are several methods for doing it.
You could create a 2 computer network if both systems have NIC cards (Network Interface Card). You specify on each computer which drives or folders you want to be shared between the 2.
Or, you could use a USB cable to link the 2 computers. You need a special USB PC link cable and you would have to start up a small program on each computer whenever you wanted to share files. Both computers would have to have available USB ports.
It is also possible to set up a network using the two computers serial cable interfaces.