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Unfortunately, taken in context, "low distortion" might actually be the case because it can be very hard to eliminate distortion in a wide angle lens. One of the most remarkably low-distortion wide angle lenses is the Zeiss ZM 21mm f/4.5 C-Biogon. No other 21mm prime lens comes close; they all have strong wave distortion.

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All zooms have distortion, sometimes pronounced. A zoom usually has barrel distortion at its widest angle of view (shortest focal length), and pincushion distortion at its narrowest angle of view (longest focal length), with some some happy middle area having little or no distortion.

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The graph below shows distortion for the Zeiss ZM 21mm f/4.5 C-Biogon (for the Leica M9). This is as distortion-free a wide angle prime lens you'll ever find.

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Pincushion distortion makes an image bow inwards, the image looks "pinched". Pincushion distortion is generally less acceptable visually.

Shown below is an image from the Zeiss ZE 21mm f/2.8 Distagon, which has wave distortion, see its distortion graph further below. Observe the pinching upwards effect in the corners at top left and right: this is pincushion distortion. The barrel distortion over most of the frame is less obvious because it covers a wider area. Wave distortion is usually acceptable, but can be an issue for man-made structures like this.

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One of the sillier claims you might see is that the amount of distortion for lens X is "undetectable by the human eye". This is a nonsense claim typically made for wide angle lenses— don't believe it, the human eye (brain) is very good at seeing distortion on regular subjects, such as architecture.

The graph below shows distortion for the Zeiss ZF.2/ZE 21mm f/2.8 Distagon. This is typical for a lens in the 21mm range: a pronounced wave-type distortion which manifests as barrel distortion over most of the frame, followed by a reversal to pincushion distortion.

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To master the topic of lens distortion blah blah blah, please consider our publication Making Sharp Images. Making Sharp Images expands significantly on this and many other related optics and technique topics, and is a unique and economical way to upgrade your understanding and effectiveness at image making.

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Shown below is the Nikon 24-70mm f/2.8G at 24mm. Mouse over the image to see the Nikon 14-24mm f/2.8G. The 14-24 is all but distortion free, whereas the 24-70 is strongly bowed with barrel distortion— unacceptable for some purposes in my view.

Some lens manufacturers (eg Leica and Zeiss) provide distortion graphs for their lenses, very helpful in determining applicability of a lens for certain types of photography, such as architecture, product photography, etc. Nikon and Canon do not provide such graphs.

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Wave distortion ("moustache" distortion) manifests as barrel distortion to the edges, then pincushion distortion to the corners. Straight lines are particularly noticeable with wave distortion, think of a distant horizon.

Barrel distortion makes the image bow outwards, like a barrel. Barrel distortion is generally more acceptable visually than pincushion distortion.

The graph below shows distortion for the Zeiss 50mm f/2 Makro-Planar. This is a good performance, about half that of a 50mm f/1.4 design, but still enough to be bothersome for some subjects.

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