Difference between "aim" and "purpose"

The explanation in the dictionary of an "aim" is

The aim of something that you do is the purpose for which you do it or the result that it is intended to achieve.

and the explanation of a "purpose" is

The purpose of something is the reason for which it is made or done.

So are there any differences between "aim" and "purpose"?

And which word should I fill in the blank? "But for the _____of communication, we dress in clothes of different colors."

In Koine Greek, both would be telos, but in modern English, the weight of meanings would tend to prefer purpose here.

Purpose is strictly a noun - It tends to adhere mostly to the reason behind an action or thing. e.g. The purpose of X is to Y.

Aim, on the other hand, can be both a noun and a verb. Typically the first thought with aim is to point, as in a gun. In other words, I'd aim my weapon at the target. And, as a verbal noun, the aim of an organization can be that thing on which they are focused. But, it is usually less of a "reason" than a direction.

For that reason, since you are taking about the reason for communication rather than its direction, I would use "purpose".

And, as the RedDwight suggests, "for the purposes of" is pretty much idiomatic.