Colorize vs Colo[u]r
> two words for the same concept
There is a difference in meaning. To say something is "coloured" would imply it has always been that colour. To say something is "colorized" tells you that colour has been added. One (usually) describes a state, the other describes a process. Sometimes it is helpful to choose the right word to make a precise statement.
> with little understanding of the rules of syntax and grammar
I think you will find that the use of the -ize morpheme to produce a verb from a noun is pretty standard (e.g. standard -> standardize).
In fact, some pedants prefer this to the alternative of simply verbing a noun.
> a process that applies only to film
Yeah. Right. We are not allowed to extend the semantic domain of words. I think that applying the same term to the processing of computer generated images is only a small step from applying it to film (which probably has to be digitized first anyway).
> a trademark
So what. Some trademarks are words, some aren't.