Yeah, the Aira is clearly a softsynth. What makes a 303 distinct (and this is to some extent mirrored by a x0x) is the brutal simplicity of the circuit. These things are very very primitive and there are sonic qualities gained by the lack of complication. Here's a video of parallel 303 and x0x, both of which are from an era where circuitry was through-hole components on a larger scale than we do currently. https://www.youtube.com/watch?v=wkJk_BpqHzQ

There's also a modern version called x0xheart which is more SMD components, and it has yet another sound: sort of more surgical and pristine than the older through-hole builds, but still distinctly NOT a softsynth. This is a x0xheart: https://www.youtube.com/watch?v=lgBa2d7gsPo

Hardware hackers who like acid music are heartily encouraged to explore this sort of thing! If nothing else, the modding scene around 303s is great fun :)