:after vs. ::after

Is there any functional difference between the CSS 2.1 :after and the CSS 3 ::after pseudo-selectors (other than ::after not being supported in older browsers)? Is there any practical reason to use the newer specification?

It's pseudo-class vs pseudo-element distinction.

Except for ::first-line, ::first-letter, ::before and ::after (which have been around a little while and can be used with single colons if you require IE8 support), pseudo-elements require double colons.

Pseudo-classes select actual elements themselves, you can use :first-child or :nth-of-type(n) for selecting the first or specific <p>'s in a div, for example.
(And also states of actual elements like :hover and :focus.)

Pseudo-elements target a sub-part of an element like ::first-line or ::first-letter, things that aren't elements in their own right.

Actually, better description here: http://bricss.net/post/10768584657/know-your-lingo-pseudo-class-vs-pseudo-element
Also here: http://www.evotech.net/blog/2007/05/after-v-after-what-is-double-colon-notation/

CSS Selectors like ::after are some virtual elements not available as a explicit element in DOM tree. They are called "Pseudo-Elements" and are used to insert some content before/after an element (eg: ::before, ::after) or, select some part of an element (eg: ::first-letter). Currently there is only 5 standard pseudo elements: after, before, first-letter, first-line, selection.

On the other hand, there are other types of selectors called "Pseudo-Classes" which are used to define a special state of an element (like as :hover, :focus, :nth-child(n)). These will select whole of an existing element in DOM. Pseudo classes are a long list with more than 30 items.

Initially (in CSS2 and CSS1), The single-colon syntax was used for both pseudo-classes and pseudo-elements. But, in CSS3 the :: syntax replaced the : notation for pseudo-elements to better distinguish of them.

For backward compatibility, the old single-colon syntax is acceptable for pseudo-elements like as :after (browsers still all support the old syntax with one semicolon). Only IE-8 doesn’t support the new syntax (use single-colon if you want to support IE8).