I have to confess, I don't really see them as separate things. I just see them as the same thing but with a different time perspective.
For me, Saving is more long-term and money I do not plan, or think I will need, in the near future. So that usually means longer-term investments.
Investment can be anything from short to long-term. But I guess the key difference for me is that I need to be able to access these funds fairly quickly.
Atleast that's how I see the main difference.
RE: Finding the balance between your Savings and investing