Afterward versus afterwards -- which, and/or when?

Afterward[s]: As someone with a background in British English who has studied and lived in the US over the past four years, I would say that "afterwards" is more commonly used in the British, while "afterward" is chiefly found in American usage. To confirm this, I sampled various dictionaries online, both American and British.

However, this does not always follow for words such as "forward[s]", "backward[s]", etc. I will deal with each case separately, treating them all as adverbs:

Forward[s]: The form "forwards" is rarely ever used in today's English, whether British or American. With or without the "s", the meaning remains unchanged.

Backward[s]: Again, "backward" is chiefly American, while "backwards" is certainly almost always used in the British. (As an adjective, though, "backward" is the correct usage, never with the "s".)

Toward[s]: The form "towards" is the British usage, while "toward" is the American.

Suffixation: Of course, the suffix "-ward[s]" can be tagged onto any word to indicate direction, as in "heavenward", "landward", and so on. As a general rule, it is strictly "-ward" in all adjectives, while adverbs could be "-ward" or "-wards," depending on the user.

And no, the "s" does not indicate plurality.

A little research reveals that the s is not meaningless, but rather conveys the relationship between nouns in a sentence, as in 'possession (as well as other more ancient and less remembered relationships).

Ward: Old English -weard, from a Germanic base meaning ‘turn.’ The forms in -s are all remnants of the old genitive singular inflection.

English: For more details on this topic, see English possessive. Old English had a genitive case, which has left its mark in modern English in the form of the possessive ending -'s (now sometimes referred to as the "Saxon genitive"), as well as possessive pronoun forms such as his, theirs, etc., and in certain words derived from adverbial genitives such as once and afterwards. (Other Old English case markers have generally disappeared completely.) The modern English possessive forms are not normally considered to represent a grammatical case, although they are sometimes referred to as genitives or as belonging to a possessive case. One of the reasons that the status of -'s as a case ending is often rejected is that it attaches to the end of a noun phrase and not necessarily to the head noun itself, as in the king of Spain's daughter, not the king's of Spain daughter as would be expected if -'s were a case inflection on the noun king (and as was done in older forms of English).

Merriam-Webster has a useful article on this subject:

The word toward(s) is old: it goes back to the 9th century, where it was a blend of the word to and the suffix -weard, which was used to refer to a specific direction. If you go toward something, you etymologically move in the direction to that item. But from the earliest moment of toward's life, it was spelled both with a final -s and without.

They then note that later writers in the USA came to think (wrongly) that the 's' was an 'innovation' and therefore incorrect. While in the UK, no such idea took hold and the 's' form remained the most common.

The stage was set for the odd state of affairs we currently have: that toward is American and towards is British.