Generally, if someone uses the term 'distortion', they're talking about 'lens distortion', which can be 'barrel distortion' or its slightly less annoying cousin, 'pincushion distortion', both of which are the (in)ability of the lens to take photos of straight lines and keep them straight.
For almost all reviews here, Bryan's got graphs of how distorted each lens is.
For an extreme example of 'barrel distortion', look at the Samyang 14mm or the 28-300L @ 28mm. Barrel happens most on wide-angles, zooms or primes. Fisheyes do it too, but on purpose.
Pincushion is the reverse effect, lines bend the other way, it's not nearly as common or annoying (to me). Normally only happens at the long end of superzooms, check out the 28-135 @ 135mm for an example.

Vignetting is darkening of corners. As a generalisation, it's normally worse on wide-angle and or wide-aperture lenses, but it can happen anywhere. An example I'm familiar with is the wide end of the EFs 15-85. Closing the aperture down (narrower, higher f/ number) can reduce most problems. I've never heard vignetting called 'distortion' though, it's just 'vignetting' or 'corner darkening' to me.

Also, i've never heard of 'iso distortion'. Does that mean 'high iso noise' maybe?

And I wouldn't just generalise on brand, each brand has its good and bad lenses, some better than others. The EFs 15-85 has really bad vignetting and barrel distortion at 15mm. But other than that, it's in the top 2 of Canon EFs lenses in that focal range. Vignetting can be fixed in DPP ('peripheral illumination correction'), and you've seen that you can fix distortion too in the 'lens correction' bit too.