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
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.