There are many types of classifications, taxonomies and standards in and around the social purpose sector. Here are a few places to find some of them!
David Kane's GitHub is always a source of good stuff. He hosts a section on charity sector classifications including ICNPO, Charity Commission, SIC codes. You can find it here
SCVO has a GitHub for their Categorisation of non-profit organisations in Scotland. You can find it here
Christopher Damm and that man David Kane are working on a tag based classification system for UK charities. You can find the current Airtable version here
https://airtable.com/shrakjlWQR60s4t34/tblcGkah3oNBLrHzP
The Philanthropy Classification System (PCS) is Candid’s (formerly Foundation Center and GuideStar) taxonomy, describing the work of grantmakers, recipient organizations and the philanthropic transactions between those entities.
https://taxonomy.candid.org/resources/downloads/full-pcs-taxonomy-with-definitions