Rectifier: changes AC to DC, these are typically part of the power supply, only.
Buffer: a circuit that provides isolation between the input and output sections of a circuit. In the case of a hybrid tube amp, a buffer is used because tubes cannot supply power to low impedance loads very well. Translated, this means tubes supply voltage, but not much current. So, in the case of hybrid tube headphone amplifiers, the buffer is usually a unity gain buffer, meaning no amplification is provided at all by the buffer, but current is often enhanced.
Hybrid tube headphone amplifiers, if designed correctly, provide a means for tubes to be used for voltage amplification, but a solid-state buffer supplies the current. Transformers can do the same thing as a buffer, usually at a much higher cost, but they can't add to the power. Buffers can add to the power by providing current through the means of its own power supply. Unless a tube provides a good amount of power at the outset, output transformers can only do so much. That's another reason why you see a lot of tube hybrids on the market, but not many output transformer-equipped tube amplifiers.
Solid-state buffers provide a means for tube amplifier circuits to supply adequate current to low impedance headphones, but the tube is always used for amplifying the voltage of the circuit.
A buffered opamp amplifier works the same way. The opamp is used as the signal amplification and then a set of opamps - or solid-state buffers - are used in the 2nd stage of the circuit to provide current. Almost every solid-state amplifier works this way, even if opamps are not used (signal FETs can take the place of opamps).
The only situation that I can think of where tubes are used as buffers is if true power tubes are used in the circuit. Almost always, you are talking about a pure tube amplifier in that case, not a hybrid. OTL tube amps simply use a small signal tube to feed headphones directly, with capacitors filtering out the DC. The output current is negligible. It's why you often hear people state (correctly) that OTL tube amps are not good for low impedance headphones. With something like a 300B tube, the current can be much greater, simply because those tubes can supply a lot of watts, but you will PAY $$$ for that capability.
A rectifier tube has nothing whatsoever to do with the amplifier circuit itself, only the power supply. Nevertheless, you will see many threads around here talking about rolling rectifier tubes for better sound. That's simply an indication that the power supply is not totally clean and the rectifier "leaks" into the signal side of the amplifier circuit, thus affecting the overall sound signature of the amp.
