Yes. FusionAuth Cloud starts with Community Edition as the base version.
You can purchase one of our paid editions for both the self-hosted or FusionAuth Cloud. Once you enter the license id for a paid edition, it activates the premium features in FusionAuth (including Breached Password Detection, LDAP support, Advanced Registration Forms).
You always get the same features whatever level you are at no matter where you host. That is to say, if you have a premium plan, you can host or we can, the features are the same. If you use the community edition, the features are the same no matter where you host.