Let's clarify the word polyphony for firstly:
Polyphony is usually described as 2 or more (poly means many) separate synthesizer voices ("phony") able to operate independently. You can have 2, 3, 4, and many more voices. Synthesizers or patches said to operate this way are described as being Polyphonic. A voice is usually considered a block of functionality that usually provides at the bare minimum on/off (gate) and note (frequency) controls. Often a synthesizer voice may have other parameters to be controlled as well. Synthesizers with many independent, but drastically different sounding parts, are called multitimbral (many sounds (timbres.)
I can imagine when you read about Axoloti patches here they're describing single patches that have many voices and form a complete instrument. A basic keyboard you may have played before (eg. an organ) would mimic this behavior.
To continue.. A synthesizer (or patch) that can only produce one unique sound at a time is considered to be monophonic. (mono meaning one) and phonic meaning voice or sound. I think you referred to them as homophonic - and sounds can be homophonic (2 or more sounds that sound the same) - but one voice/sound is called monophonic. There are many great monophonic synthesizers out there and they're the simplest form of a synthesizer to build and operate.
Generally you can recognize a polyphonic synthesizer patch by listening for chords - 2 or more notes that sound in harmony (similar to a guitar chord). You may hear a monophonic synthesizer sound by listening to voices sounding on their own - like a lead guitar solo.
These are only rules of thumb - simple ways to hear things - they may not be accurate in all cases.
Other words for you to investigate: paraphonic, multitimbral.
Check out wikipedia, youtube, or other syntheszier and electronic music forums for more resources.