I used dyndns.org for a while when I ran my own mailserver/webserver at home. Very reliable, and now most home NAT routers support it within thier configuration (at least my Linksys stuff does) so it's almost idiot proof.
as long as references to your server(s) is done through URLs and not IP address(es), there should be no difference. dynamic dns is used in situations where there is a need to assign an fqdn to a dynamically assigned IP address host. when the IP address changes, dns is updated "dynamically".
dyndns.org is a dns hosting provider that offers dynamic dns hosting (in addition to "regular" dns). personally, i like them as dns hosting is all they do and their servers are geographically well distributed around the planet. if you're using dynamic dns, you'll need a provider such as dyndns.org as domain registrars and isps don't offer such a service (afaik).