Hi Ralph!

I see that it's the img=right and img=left commands that do it.

Yes, in this version (the 2.x branch of mlf).

Strange, I've found that one mlf forum uses img|left and img|right,...

[img|left]foo[/img] and [img|right]foo[/img] is the syntax in the 1.x branch of mlf.

... while some BB Code forums don't apparently even allow the usage of left and right

If you are talking about mlf, you only have the option to allow BBCodes for images or not. Once you allowed them, left/right is always 'onboard'.
BTW, 'left' is default: you don't have to explicitely use it in order to get text floating to the right of an image aligned to the left.

... maybe the separator character doesn't matter..?

Oh yes, it does.
If you use mlf 2.x syntax in mlf 1.x, the BBCode is not rendered into XHTML and displayed as plain text, like:
[img=right]foo[/img]
The same is true if you use 1.x syntax in 2.x, getting only:
[img|right]foo[/img]

Probably Alex has changed the syntax to fit into Christian Seiler's BBCode parser class. The syntax used for images in the 2.x branch is more consistent with other BBCodes, which all follow the scheme of '[color=#00f]parameter[/color]=[color=#00f]value[/color]'.

A list of implemented BBCodes are given here.