URL change /migrate blog

Here’s the deal. My website is http://www.whateverURL.com . On that same host, I have http://www.differentURL.com as a parked domain. I have a WP blog installed on my main domain as the default index.

I’m interested in either migrating my blog over to http://www.differentURL.com as an add-on domain, which would just involve moving the blog. Or else actually changing my main domain to the new one, which would probably require my server. In any event, what steps does a person need to take to move their blog to a new host?