Rescue/Engine: anything requesting a fire truck or rescue truck.
Quint: anything requiring a platform or fire truck.
Pumper/Tanker: anything requiring a tanker or fire truck.
Platform will only respond as a platform truck, it will not as as a fire truck.
Not sure type 1 or 2 engines.
Mobile command can act as a chief of a MCV.
Utility will act as a rescue for certain calls.
A Heavy Rescue/Boat combo unit will act as a rescue unit.
A personal transporter also acts as a heavy rescue I do not. Own any I have just heard this one.
Those are all the ones I know off the top of my head and can type while mobile.
If you send a multi purpose unit such as a quint to a call it will act as both a fire truck and platform. Example: smoke investigation call requires 1 platform 1 fire truck and 1 chief. If you send a quint and a chief that will clear the call out.