Just like you can play an audio tape in a video tape player, not all tapes work in all systems. There are several formats - the most popular are probably DDS, DLT/SDLT, LTO, and AIT. There are others as well, but these are the most popular. Each of these tape types are physically different. The numbers generally define the "Version" of the tape - higher versions hold more data. How much depends on the tape technology. Generally, between 50% and 100% more than the last version. In MOST cases, tapes are backward compatible at least for recovery. Meaning a drive that supports LTO3 will be able to recover data recorded to an LTO2 drive.
In general, if you have questions about tape types/technology, I would suggest you review their wikipedia entries - for example:
LTO -
http://en.wikipedia.org/wiki/Linear_Tape-OpenDDS -
http://en.wikipedia.org/wiki/Digital_Data_StorageDLT -
http://en.wikipedia.org/wiki/Digital_Linear_TapeAIT -
http://en.wikipedia.org/wiki/Advanced_Intelligent_Tape