The ER tap collets are available for both metric and inch sized taps from a number of different companies. That photo in question on the PDF of the Verdex tapping collets is just a bad one. Every ER tap collet that I've ever used certainly DID grip the shank of the tap and just drive the square, not grip it.
With taps, we need to know that there are many different types of shank standards for the shank diameter and the size of the square drive. Most inch taps adhere to ANSI standards, most metric taps adhere to DIN standards, and there are a great many taps that have a hybrid DIN/ANSI design. Those taps have the DIN style configuration, usually (but not always) of a short thread length with the reduced diameter neck, though the shank diameter and square size are ANSI standard size. Here's 3 taps. The middle one is an ANSI standard, the other two are pure DIN style.
In the photo below, the two pairs on the left are DIN/ANSI shank dimensions, with what is known as a "reinforced" shank. The one on the right is pure ANSI spec, with what is known as a "passing through" shank.
It can be very confusing and is the reason why using tap collets can get expensive. You not only need to match the collet to DIN or ANSI specs, but also need to know the style of shank for a given size and style of tap for which you are planning to get a collet. Then, as an inevitable result of tooling up the proper way at great expense, you break the tap and end up using your tap wrench with the dull old hand tap you found at the bottom of your toolbox. ;)