A synthesizer is generally a higher-level ready-to-use product containing any number of oscillators, sequencers, and other circuits and bells and whistles under the hood. A device with an oscillator and a sequencer qualifies as a basic synth.

At a lower levels you find modules like sequencer, oscillator, etc. They are generally not used by themselves: you plug a sequencer into an oscillator to make use of it, just like a standalone oscillator by itself simply makes a continuous noise that gets old quickly. A synth does that connection for you and exposes the controls.

(To make things even more fun, the lines between lower-level audio modules are often blurred. For example, the difference between a sequencer and an oscillator can be best summed up as: the former is commonly designed for unipolar control rate signal change where you can specify exact level per step, while the latter is designed for bipolar audio rate signal change between two predetermined extremes—however, as the “designed for” hints, you could configure some sequencers to output a bipolar signal changing so fast it is audible, just like you could run a square wave oscillator so slowly that it becomes a 2-step sequencer.)