Well, the difference is mostly semantic but this is a good way to reveal minor differences in definitions that are not inherently obvious. If you see them as the same than they are same for the purposes of the conversation which is all I needed to know. :)

The reason I asked for clarification is that this sentence:

Evolution designed us to value things but it didn't (can't) give us a reason to value those things.

Can be read by some as:

Evolution [is the reason we] value things but it didn't (can't) give us a reason to value those things.

To which I immediately thought, "Wait, if it is the reason, why isn't that the reason?" The problem is just a collision of the terms "design" and "reason." By replacing "design" with "cause" and "reason" with "purpose" your meaning was made clear.