Not to be confused with electronic drum kits/modules, drum machines are synthesizers that focus on drum and percussive sounds. Again, there are both analog and digital options. Analog drum machines use filters and envelope generators to shape waveforms into punchy tones with plenty of attack. Digital drum machines either do the same with digital waveforms, or simply use samples of existing drum sounds.
A sequencer can be used to send information to your synthesizer. This could be a rhythm, a repeating pattern, a melody, or all of the above. If your synth doesn’t have a keyboard, a sequencer is a great way to control it. Alternatively, if you simply want to step back from playing, and instead experiment with effects and dynamics, a sequencer will take care of the notes so you don’t have to.