How to define profile types per group type in the Group module?
... can I define a profile type per group type?


Sure (yes?) you can, it's what in the Group module is called "Group Specific Roles".


  Group profile types seems to be global ...


Here you're talking about what in the Group module is called "Special Global Role" or "Configured Global Roles".

For more details on this, refer to the answer to "What are the various roles supported by the Group module?".

Be aware: this answer applies to D7, as in the question (for D8 it would be different ...).