Hashtags are mostly used as unmoderated ad-hoc discussion forums; any combination of characters led by a hash sign is a hashtag, and any hashtag, if promoted by enough individuals, can "trend" and attract more individual users to discussion using the hashtag.
The tag you are talking of in this context is a keyword/index tag
An index term, subject term, subject heading, or descriptor, in information retrieval, is a term that captures the essence of the topic of a document. Index terms make up a controlled vocabulary for use in bibliographic records. They are an integral part of bibliographic control, which is the function by which libraries collect, organize and disseminate documents. They are used as keywords to retrieve documents in an information system, for instance, a catalog or a search engine.
Going by these definitions, if you want to curate the information then go for tags. For a freeform approach, use hashtags.
The use of hashtags is in the social circuits where there is no need/possibility of curation and the same tags permeate multiple platforms. There is no notion of synonyms and other moderations making it extremely versatile to use and search for.
Tags on the other hand are much more structured, they have definitions and guidelines on when to use which one. They are populated and maintained by a community.