(It could be different in other German speaking countries)

"Garni" comes (I think) from "garnieren" (ausstatten, schmuecken).
"Hotel garni" (I only know this order of the words) is a hotel without restaurant that only provides breakfast just like a "Pension" might do. The difference between "Pension" and "Hotel" is only the status of the owner. The owner of a hotel has no other (relevant) income than the hotel but the owner of a "Pension" (pronounced the French way) has another main income.

A farmer for instance also renting spare rooms to tourist has a "Pension". Therefore a Pension is usually smaller and less expensive than a Hotel. I'm sure there are less regulations to follow forthe owner of a Pension but I don't know which additional regulations are there for a hotel.

Wolfgang