activated carbon takes care of vapor phase and solid filter takes care of particulate (i.e. condensated dust from smoke), theoretically speaking, however the carbon mesh itself will act as a mechanical filter in addition to a chemical filter..
but I am not sure, there is also something called a molecular sieve behavior to think about. but the carbon also does something in terms of chemical reaction more so then a simple molecular sieve. and there are also electrostatic effects (this is how a simple respirator works, i..e standard issue n95).
Usually cheap ones are a carbon, expensive ones are a hepa + carbon,
you could get a 60$ benchtop air purifier from honeywell that has carbon inserts. works fine for my 3d printer to keep smell away
so when you use flux, you have alcohol, which is a gas, that chemically interacts with the carbon filter, then smoke which is a particulate and vapor and some distribution of particles formed by the smoke will require a filter beyond carbon filter's crude filtering capacity to filter out.
so it all turns to gas the solidifies into small particles but the alcohol stays a vapor for a while, or something like that.
Also would say if your lab space is small, the bench top air purifier is a good choice because you can also use it to neutralize the smell of commonly used things like epoxy, silicone, cleaning alcohol.. the only problem with them is that they don't have the heavy suction of a solder fume extractor, so some stuff might get out unless you take some measure to channel the smoke.
Good idea if you plan on using stronger glues.. after you use it a bunch epoxy can sensitize you. Also of course it keeps down on super glue and cleans the air from a lab printer. And of course you might forget to clean some nasty eBay buy, and have it shoot dust out when you turn it on.
this one is a good value IMO
https://www.honeywellstore.com/store/products/honeywell-portable-hepaclean-tabletop-air-purifier-hht270w.htmIf you want to make a home made one, and only use carbon, you will get rid of the smell but some particles may get through (invisibly small). If you go for hepa, the filters are sized for appliances, so even if you use cheap building materials, I don't think you would save much, especially if you build it nice (say polished wood for the interior so its cleanable).
If you build it, you need to be precise, its like a gasket, so you need to make sure the filter sits properly and there is no air flow around it, a common mistake might be to make it too weak so it bends under suction flow and forms a gasket leak. And there is probobly a rule some where that tells you how to use tracer smoke to test it, because the problem is it might capture all the visible heavy particles, but not the invisible lighter ones, so I assume you would have a test where you generate smoke (i.e. dirty fire with rubber) and look at the 'whisp' that it forms while its going into the filter, and gives the visual appearance that the filter is over powered (i.e. the visible smoke only reaches 50%* filter inlet height). A powerful columinated light may allow you to inspect the outlet stream for particles big enough to be detected as reflectors under strong light).
*i don't actually have a figure, its just a number i made up to make a point
**seals are particularly imporant for a solder fume extractor, because it has a higher suction, its more noisy, so you will only want to use it for soldering, not as a room air purifier, so if that is your only purifier, it needs to capture everything in 1 go, wheras what happens with a room filter is it keeps recirculating air, so you reduce efficiency of the filter, but it can still bring it down to some good level after a while, because statistically all the stuff will hit a filter after enough cycles through the machine. If you just power a extractor on for the duration of soldering, and power it off, anything it does not capture at that point will not reach the filter, and it will stay in the room until it settles or is replaced by fresh air.