AFAIK there are four basic products in the Topaz AI range - I only have
Denoise AI, though
Denoise - removes noise (and can do a little sharpening as part of that)
Gigapixel - enlarges images (adds pixels, increases resolution to allow you to print bigger or get away with radical cropping)
Sharpen - sharpens and recovers detail by guessing what an in focus image should look like, but doesn't actually increase the number of pixels in a file. Its party trick is recovering shots that are actually out of focus.
No surprises based on the names
Photo AI is relatively new and does all of the above in one application, which would certainly be more convenient.
However it does so with less control than each of the dedicated apps - I saw this video that walks you the differences a couple of weeks ago and found it useful.
View: https://youtu.be/SMgGRDx8wGY
I'm still on the fence about Photo AI as a result. I know with Denoise that I need the level of control that it gives me. YMMV.
For my purposes, Denoise is occasionally
very useful when I have noise that Lightroom cannot easily deal with. I keep eyeing Gigapixel as it looks fantastic, but I find it hard to justify the cost for the very rare occasions I would really
need it
. Lightroom's scaler is generally 'good enough' for me. Most sharpening I can deal with well enough elsewhere and broadly I try not to take pictures that are poorly focused! :-D
Add all that up and Photo AI doesn't look terribly compelling, so I shall probably stick with just Denoise AI.