It can all get confusing; especially when you're trying to respond online with any clarity. You never quite know how your terms are going to translate over the Internet. For example, I immediately think of convolution reverb in terms of an impulse. And it was a lot easier when hardware processed with PWM, or by skewing sawtooth waveforms for sound variations.
I would personally prefer 'oscillator-based', but those lines have blurred since the carryover from original hardware synths. Cakewalk synths present unique challenges. You can create an oscillator from a long 'sample'. And an oscillator really is a short 'sample' of a repeating waveform. Waveform-based might be the clearest term, but then you run into the .wav file format that - you guessed it - many longer samples are contained in.
RGC used 'wavetable' for the Dim Pro/Rapture family. Now you run into the confusion with the PPG wavetable-scanning synths. I don't know what the answer is here. It's like the preset/patch debate. What is it - the 'macro' of the entire synth output? Some portion / element of the synth? We rarely use patch cables any more. So, is an LFO 'preset' a patch, or a preset?
I guess that's why you rarely see any short postings from me. I always err on the side of an over-abundance of information; just to get the point across. Which - in & of itself - leads to more confusion ...