I must have two URL (ex: world wide web.mycoolsite.com and world wide web.myfunsite.com) and point these to exactly the same server, and employ a few of the same files. I would like another home page and css for every site, but evernthing else could be identical.

My webhost enables me to 'park' a website, but that changes the URL the user sees and I am unsure if there's anyway to identify which URL the consumer initially joined.

Any ideas how this can be done?

I believe you'll need a HTTP 301 permanent redirect. Example