That is not quite right. In Postgres, timestamptz (aka timestamp with time zone) represents an instant in time. timestamp (aka timestamp without time zone) represents what you are calling local time. timestamp (without time zone) is exactly what you should use to store future appointments.

Something that often trips people up is that they think timestamptz stores a timestamp plus a time zone (probably because of its unfortunate name). It does not; it always stores a Unix epoch without an extra time zone, converting any zoned timestamp that it is passed.

Yes, you are right.