The best way to determine what a tag is being used for (on a per-site basis, when there is no description) is to look at the first few uses. A suggestion, just a hint, comes from how it is used on other sites; it expected and reasonable that each site would use the tag in a manner focused on the site's subject, relatively few tags are duplicates amongst all sites.
Some key advice is offered on the Operations Research Meta:
"How can I edit tag wiki entries?":
"When you are the first person to create and use a new tag it's considerate to at least write the excerpt for the tag so no one has to guess what it's used for and the possibility of use for multiple meanings is avoided.".
A short answer to your question is:
The participation tag is about participation (positive, interaction between people and the community). About people doing work along with passively reading.
The user-engagement tag is about holding the interest of the community (probably positive, but it could be about getting people to read and follow a rule or change that may not be well received). More about getting people to visit and read, over doing work.
The user-behavior tag is generally about discussing expected behavior or announcing non-negotiable behavior; reading, writing or voting not required.
When discussing negative behavior the problem-users tag can be added to the above tags.
When discussing positive behavior the expert-users or experienced-members might be used; but neither has a wiki entry.
A single tag doesn't have to cover every situation, sometimes 2 tags must be combined.
Use the correct tag markdown for the correct site: [tag:tag-on-main] or [meta-tag:tag-on-meta] .
You are free to, and encouraged to, edit the tag wikis. If you write a good description that is deemed correct you should expect it to be appreciated and approved, failing that it will be rejected the same as any other edit (but often by people with higher reputations).