Yes. Custom flags for moderator attention are seen only by moderators. The rest, while visible to moderators, do touch the wider community in some fashion, such as by placing the post into a review queue.
Spam and offensive flags often do not require moderator attention to handle. Six such flags will result in the post being deleted and a -100 reputation penalty applied to the owner of the post.
"Very low quality" and "not an answer" flags place the post into the Low Quality Posts review queue. Such flags may be marked as disputed if reviewers disagree with the flag (e.g. a reviewer hits Looks Good on a post that was sent to the LQP queue due to a VLQ flag).
Closure flags (e.g. duplicate, off-topic, too broad) place the post into the Close Votes review queue, and can be marked as disputed if enough users click on Leave Open when reviewing the post.
Custom moderator attention flags do not cause the post to go to any queue other than the moderator flag queue, and are handled exclusively by moderators and Stack Exchange employees.
In all cases, a moderator can act on the flag directly, bypassing the community process, but Stack Exchange is designed so that the community takes up the bulk of the day-to-day moderation work.