Database for storing/sorting/sharing information?

I’m interested in setting up a database to store information that can be sorted by tags/keywords. Here are two examples: https://www.ewg.org/skindeep/ and https://www.pfaf.org/user/plantsearch.aspx. How does one do this? Is there a user-friendly software that could help me do this? If possible, I’d like to embed it on a page on my website. Maybe I could do that with a iframe?

Thoughts are welcome.

Thanks.