Is it wise to call a transistor an amplifier or rather a variable resistor?
definitely yes, a transistor is a current amplifier, not a variable resistor at all …. of course, this only applies to devices bjt …
a variable resistor is the easiest to understand. the wording of the question implies a simple to understand.
while a memo from the Bell labs called him a member of the varistor class. I would not call this a variable resistance like the ebers-moll model, which I do not understand, does not show it as such but as a more complex thing. calling it a variable resistor sweeps the complexity under the carpet.
Unfortunately, the question itself mixes metaphors of concepts. the basic concepts of amplification and resistance make it more difficult to choose what is most applicable to the transistor concept.
I will try to keep the at a high level rather than delve into the details of the transistor theory.
The simple is that both concepts are applicable, but with the ubiquitous nature of computers, I lean toward the switch (as in the logic gate) as the most common metaphor for a transistor. after that, maybe an amplification. to consider the variable resistance as a transistor concept, it is necessary to delve deeper into the fundamental operation of the transistor. the bipolar transistor juntion (bjt) is a current-controlled variety and the field effect transistor (fet) is a voltage-controlled variety. both are used in amplifier circuit designs (and others). the engineer / designer chooses which type, based entirely on what he is trying to accomplish.
If you’re trying to understand how to design transistors in their most basic version, it’s probably best to think of them as voltage controllers or current controllers (bjt vs. fet). Conceptually, both are known as active devices designed to limit a single fundamental electrical concept (current, vs. voltage). while amplification is a higher level concept that has multiple components of what you are trying to amplify. This usually involves a complex signal that contains both current and voltage, as well as many other considerations.
Keep in mind that a transistor by itself (without support components) can not work. for example, at a minimum, you must limit the current flowing in a transistor, otherwise it will self-destruct in an instant.