DAC- digital to analog converter, like your soundcard.
DAC has usually already analog to analog amplifier in it.
Amplifier has or could have no DAC e.g. analog to analog amplifier.
Some people say DAC also as an amplifier or complete amplifier unit to simplify things but this create confusion.
Sound quality is determined mainly by your end driver a.k.a. speakers or headphone.
You get 80% of the sound quality from this.
If you want to get the next 20%, you have to get a good DAC+amp, especially if you use those high-impedance headphones, since standard on-board soundcard does not have strong enough amplifier to drive them.
Special headphones like wireless headphones, etc. already have their own electronics incl. amplifier or complete dac+amp unit.