transconductance is (change of drain current)/(change of gate voltage).
BJTs, FETs (and vacuum tubes) are basically voltage controlled current sources so "transconductance" is a measure of performance and is the amount of output current change versus the amount of input voltage change. It can not be called gain. Gain is Vout/Vin, Power out/Power in, or Iout/Iin and does not make sense with Iout/Vin. Once a circuit with a BJT is designed it's O/I may fit one of the definitions of gain.
From wiki: Transconductance is a contraction of transfer conductance. The old unit of conductance, the mho (ohm spelled backwards), was replaced by the SI unit, the siemens, with the symbol S (1 siemens = 1 ampere per volt).