For synth there are two common pedal approaches-
the first approach just uses your input sound to calculate pitch, note on/off, and dynamic information and then plays an actual digital synthesizer algorithm that attempts that follows all of those pitch/dynamic calculations. The plus side of this approach is that you get accurate actual synthesizer sounds and some of the options in this category (like the Future Impact and C4) have a really wide variety of sounds and tweakability on tap (4 different tunable synth oscillators at once, versatile filter sections, etc). The downsides to this approach are latency (it takes time to calculate the pitch of your input signal, plus time for other general processing) and potentially funky tracking (most of these options are monophonic and can play the wrong notes, miss notes, or play extra notes depending on the signal you feed them and so tend to require a lot of setup trial and error and learning to “play to the pedal”).
The second approach are pedals that take your input signal and manipulate it directly into something that resembles a synth waveform that can then be played through filters and other effects to emulate a synth. Analog octavers like the Boss OC-2 fit into this category (the timbre of the -1 octave is in the ballpark of a filtered square wave sound due to the way the octave is created from your original tone), as do some digital synthesizer pedals like the Boss SY series (which do some similar magic plus to the OC-2 plus a lot more but in the digital domain and have built-in filters and other goodies) . The positives from these pedals are very little to no latency (since pitch doesn’t need to be tracked) and usually no missed/doubled notes (though you can get octave up glitches from something like an OC-2 if the harmonics from your input tone overpower the fundamental too much), and digital pedals like the Boss SY series are polyphonic so are very forgiving to different playing styles (the OC-2 and other analog octavers are still monophonic and so will require some careful “playing to the pedal”, though less than pedals like the C4 or Future Impact IME). Downsides to this approach are generally less accurate synth timbres (everything in this category is instead an approximation of a synth waveform sound and the sound will vary depending on what you feed it), and usually less versatility (because your input tone is making the output tone you can’t get synth sounds that sustain longer than the sustain from your bass for example without a “freeze” type effect like some of the Boss SY pedals have) and among the analog options you are usually stuck with only a single synth “voice” and usually need a chain of pedals to get more versatile synth sounds (a common analog synth chain might be 3-4 different pedals, like Octaver-fuzz-filter-chorus or similar). The EHX Bass Micro Synth is a rare analog option that has multiple mixable voices and a built-in filter, though it has a tone that is very distinctive to itself (of you like what it does there is very little out there that can match it exactly).
I have a bunch of the options from category one, and would definitely recommend the Panda MIDI Future Impact v4 (VIP or the big-box version) out of all those options. I end up using category two options more often (usually analog synth chain options like an OC-2 into fuzz into filter into chorus) live though because of the tightness and immediacy of tracking that it gives me, even at the expense of (quite) a lot of versatility. The current update of the Future Impact is pretty dang impressive though, and IMO the best “actual synth triggered by a bass” system you can get these days, and the tracking is pretty freaking fast and accurate to the point that it might become a more permanent live pedal fixture for me!