"They got the ftp" doesn't quite mean anything. Do you mean they got the username/password used for FTP access to the files that make up the web site? Not all web sites are accessed that way (thank goodness, in this day and age, because FTP is not a secure protocol).
Changing the DNS is external, and therefore doesn't usually count — but it would be legitimate to say the website's DNS was hacked.
Changing the password is fine if you can be certain that you know what was done. But how do you know they didn't use the local unprivileged ftp access to escalate to root/administrator access? With that access, they could install a very hard to detect kernel-level backdoor. Even without root access, are you sure they didn't leave a trap in some of your files?
The same goes for database access.