Why The prefix trans- (transmitter) plus -ceiver (receiver) says it directly: a transceiver is one box that both transmits and receives, usually sharing circuitry such as the VFO, filters and antenna connector between the two functions. Nearly every modern amateur radio is a transceiver, which is why you press PTT to switch the same unit from receive to transmit.
Watch out The choice about converting frequencies to another band describes a transverter, which takes a transceiver's output on one band and shifts it to another, and the impedance-matching choice describes an antenna tuner.
TRANSmitter + reCEIVER = TRANSCEIVER. Transverter is the one that 'converts' bands.