Sunsetting to me implies that existing users may continue using it for an indeterminate amount of time, with or without ancillary services, but that the team/business has moved on and no one should pick it up. There may, or may not be, accommodations for existing users to either continue using, or migrating to another service.

To continue in analogy land, the sun has set, the store is technically still open because there are people inside, and they are not being kicked out, but you shouldn’t, or won’t be able to, come in as a new customer. It also implies that the people in should know it is getting dark outside and should maybe find their way home (or to the bar).

A shutdown instead implies a hard deadline after which the service will no longer work.

To give examples:

• an email service that is sunset may still allow existing users to receive or send emails, but will not allow new sign up. It may, for example, retain the email services to facilitate migrating to another provider, and otherwise allow setting up address forwarding. If it was a paid email account, then I would expect to continue paying, or at least for the service to continue up until renewal time, with renewal impossible.
• an email service that is shut down will stop allowing users to receive and send emails by the shutdown date. I would not expect email forwarding to another provider. Archive access may or may not be provided after the shutdown date. Service will terminate. Any money exchange for this service would end at the specified dates, and refunds, if necessary, should be handled for anything after the shutdown day.