Monosynth/polysynth
Monosynth/Polysynth refers to how many voices a synth has, ie, how many notes/pitches it can generate simultaneously. A monosynth is only capable of generating a single note at any one time. A polysynth can simultaneously produce multiple pitches in accordance with how many voices it offers. This allows it to create a polyphonic output - ie, chords.
Modular/semi-modular
Modular/semi-modular are types of synthesizer that can be rerouted by the user. Typical self-contained synthesizers - a Minimoog, for example - are pre-wired, so the connection between its oscillators, filters, amps, etc cannot be changed by the user. A modular synth is made up of totally distinct elements - aka modules