DisplayPort is an industry standard that Apple has adopted and made smaller. Mini DisplayPort is just DisplayPort in a smaller form factor. It's the exact same deal as Mini-DVI versus DVI.
However, while it's easy to find Mini-DVI to DVI adapters, it's not currently possible to get Mini DisplayPort to DisplayPort adapters, meaning that unless you build your own cable, you can't physically connect Macs with MDP outputs to monitors that only have normal-sized DP inputs.
There's no problem as far as signal compatibility goes, since MDP carries the same data as DP, it's just the physical size and shape of the connectors that's the issue. Doubtless MDP-to-DP cables will appear eventually, probably within the next few months.