random and randomised can both be used as adjectives. Random is a lemma or dictionary headword, or base word, it's the so to speak foundation onto which morphemes may be added to create variations of different meanings. According to Wikipedia the suffix of -ise/-ize is used:
usually changes nouns into verbs
However can also make verbs from adjectives, confer:
stable - stabilise - to make stable
mobile - mobilise - to make mobile
natural - naturalise - to make natural
central - centralise - to make central
Basically by adding this suffix you're creating a verb which means to do that which the adjective connotes. So to randomise is to make random.
When you randomise something it becomes randomised, (randomised being the past participle).
So the difference we have is that one word "random" is "random", and the word "randomised" acts as an adjective for something which has been made random.
That's the distinction if you want to observe one. The end result as I can see is that you end up with something random in both cases. But one emphasises that is has been made random.
In your usage I'd say the two terms are quite the same, if something is randomised then it becomes random. As I said, the difference lies in whether you want to emphasise that is has been made random. Philosophically speaking I don't know if something can be random without having been made random, I don't know.