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).