Until the Indians weigh in this may help. What they have in common is masala, which means 'spice.' Chai means 'tea' and garam means 'hot, heating.' But they're all delicious.

No -- chai masala refers to the spices used to make chai, as in tea (prominently cardamom) while garam masala refers to a pungent spice blend used across Northern Indian in savory cooking. Both masalas will vary by region and by family.