Since tagging is separated into custom tags (which people such as Moderators and Administrators may leverage to internally mark posts for some specific criteria) and user tags (which can be publicly assigned to content with the appropriate permissions), I think the best answer I can provide is "it depends". More on that below!
Giving users the ability to add tags on the community will only provide enhancements based on the utilization. That is, if nobody's adding tags, nobody else can find content using said tags! By itself, if tagging is encouraged it will encourage community participation and in-community search results will benefit as users will be able to find more relevant content.
As for SEO, adding public tags to posts doesn't hurt, but I can't say if there is a significant impact to external search index ranking. However, it stands to reason that since it is on pages that are being crawled by search engines, it shouldn't harm relevancy.
@PaulGi wrote a fantastic TKB article some time back that discusses public tags in greater detail:
About public tagging
Hopefully this helps!
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The primary difference between tags and labels are the ways they are leveraged in the community.
Tags (also referred to as custom tags) are information that users can enter to their individual posts that helps in creating a taxonomy for other users when searching for something. Any user that has the permission to do so can use tags, though if you only limit tag usage to Moderators and Administrators, you may see a specific taxonomy become generated as your "trusted" users and community managers begin using the same types of tags across many posts. More information about tags specifically can be found here:
About Custom Tags
Labels are a different type of method to create meta-categories for topics as a whole and are configured by the original author of a topic or TKB article only. This can be used to help users that are browsing the community looking for posts on a specific overarching topic, or they can subscribe to labels if there is one that they find particularly interesting. More information about labels can be found here:
Let me know if you have any questions or need any clarification!
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