Again I suggest watching this video:
Towards the end Roy Underhill does an excellent job explaining the difference between a crosscut saw and a rip saw. Essentially, a rip saw cuts with the grain (the teeth of a rip saw chisel the fibers of the wood as it cuts along (parallel) the grain of the wood) and a crosscut saw cuts across the grain (the teeth of a crosscut saw cut like a knife the fibers of the wood as it cuts across (perpendicular) the grain of the wood).
The number of teeth or teeth per inch (tpi) relates to the fineness of the cut. If I remember correctly a crosscut saw does need fewer tpi in order to get the same fineness of cut as a rip saw. For instance to get a very clean cut a rip saw may need 12 tpi but for the same very clean cut a crosscut saw may need a 15 tpi. I believe that this is due to how the saw actually cuts. Since the crosscut needs to actually cut like a knife across the fibers the natural process of cutting across fibers creates greater potential for tearing pulling and fraying of the ends of the fibers. Thus the need for a very sharp knife (aka. each tooth) as well as each knife cutting being very near to each (aka high tpi count) other in order to help compress the fibers while cutting and essentially have each knife help each other in the process.
Again, I recommend watching the Woodwright Shop episode “Sawing Secrets.” Roy Underhill’s visual aide using a straw broom, chisels, and knives to help show what a say is actually doing as it cuts is extremely helpful in understanding why it is beneficial to use different saws in different applications.