As far as I read and understand the wiki there is no (real) difference between man_made=tower and building=tower. As mentioned by @Mateusz_Konieczny there are different types of constructions possible so I would tag them differently. As a rule of thumb:
For towers primarily made from steel frames or similar (constructed very “open”) I would use man_made without building=yes. Example: Mapillary
For towers with solid walls and a roof I would tag building. Example: Mapillary
Another point: If the tower is attached to the other buildings of a fire station there are probably also used for hanging the hoses - this would indicate building or even building:part for me
I would try and may these things like “most other people do”. There are 324 tower:type=firefighter_training, and of those only one** has the combination nwr["tower:type"="firefighter_training"]["building"][!"man_made"];.