This article may be helpful
http://www.thirdsquare.com/how-to-host-a-subdomain-on-another-server-or-hosting-company-213If you use a different host for an ftp subdomain, I'd recommend going with a unix host that allows sub-ftp accounts. Most windoes hosts only allow at most a small number of ftp logins for a given account. With unix hosts, sub-ftp allows you to have many ftp accounts and assign a separate directory and login/password for each - gives you a lot more flexibility.
Don't forget to put a blank index.html page in each directory to prevent directoty listing.
Setting up mail for a subdomain on a different host than the main domain can be awkward - basically you need to add an mx record to the dns at the new host with a lower priority number that the one they automatically set up that will point back to your old mail server. It's easier to just do without mail for the subdomain.
To answer your other question - I use subdomains like blog.mysite.com or files.mysite.com on different machines from mysite.com quite often.
Anything before .mysite.com is a subdomain - e.g. www is a subdomain that by convention is routed to the same place as the domain - but it doesn't have to be. You'll see a lot of sites use www2 as a subdomain to route to a different machine. support.microsoft.com and msdn.microsoft.com are on different machines.
Subdomains have some advantages - basically, they are separate applications with their own cookies, server and application variables, and search engine indexing.
EDIT: - another useful link is at
http://content.websitegear.com/article/subdomain_setup.htm
Edited by dpyers - 26 March 2006 at 9:37am