how to classify this as a piece of software

It's a tracker combined with a modular synth in the style of Max/MSP, but also with a sequencer. Modular stuff in this vein is generally fit for live fiddling, like Reactable for example.

Unfortunately, I have a better experience with trackers in Renoise, which has dozens of decent samples out of the box, through which I can click and listen; and its effects like distortion are also much more pronounced. Sunvox seems more tailored to ‘beep boop’ synth sounds, and I'm not good with those.

would be nice to have better recording options than using the sampler

Ironically the other SDL music app, Caustic 3, has functionality for recording sounds and even a built-in audio editor. It's a very neat mobile DAW, but alas it's not being developed anymore — and its longstanding problem of only having two effects per instrument won't be fixed.