To work as an amplifier or switch, a device requires power gain. Bipolar transistors amplify current, i.e. a larger collector current is controlled by a smaller base current. A field-effect transistor controls the drain current by a voltage change on the gate.
In either case the power you can control at the collector/drain is larger than the base/gate power at the input, thus giving power amplification.
If the transistor is biased properly, and you vary the base/drain from an AC current/voltage, then then collector/drain current will vary in proportion and you have an AC amplifier.
If you change the base/drain current/voltage a large enough value you will cause the collector/drain current to go from full on to full off, creating a switch.
The maximum gain you can obtain from one stage is determined by the gain of the transistor (β for a bipolar transistor, and transconductance for the FET). These vary signicantly from unit to unit so, to negative feedback is often used in amplifier circuits to reduce gain variation.
Don't understand your question about "Variation in Q-Point due to β in FB".