I wasn't clear on if a transistor can have a collector voltage that is different than the base voltage.
One talks of a controlled current value into a base, not it's maximum safe base/emitter voltage. A series resistor is selected to set the base current to the value required, any value voltage can be driving that base resistor as long as the resistor is valued to limit the current to correct operating value. Collector current also is current controlled by the load resistance (lamp/motor/solenoid/etc) or load resistor (voltage amplifier), as max collector voltage is a safety rating not an circuit operating value.
Bipolar (NPN/PNP) ransistors are current operated devices and voltage is a byproduct specification. Mosfets are voltage operated devices with corresponding max current specifications.