this is easily done.
Look up master page branding, you can deploy a separate template on every site collection you create. You can create custom authentication, navigation, profiles, metadata, sites, you think it a different site collection is just different and can house a totally different solution.
In theory you can have 100's of site collections all with a different look and feel.
A good starting point if you want to build it from scratch.
Otherwise there are plenty of starting point master pages and templates for each content type, and plenty of advanced and simple customisations you can achieve.
You're basic topology would be:
Site collection 1 - Intranet
Site collection 2 - Extranet
You can have multiple site collections for each, I would build these maybe pointing at different subdomains but on the same server and you could even have a site collection per department if the business is large enough.
If you have any more specific questions, just ask. Sharepoint branding can be complex but it doesn't have too be. 1 google will bring back hundreds of tutorials.