A tagset is a list of part-of-speech tags (POS tags for short), i.e. labels used to indicate the part of speech and sometimes also other grammatical categories (case, tense etc.) of each token in a text corpus.
Universal POS tags are part-of-speech marks used in Universal Dependencies (UD) which is a project that is developing cross-linguistically consistent treebank annotation for many languages. The annotation scheme is based on an evolution of (universal) Stanford dependencies (de Marneffe et al., 2006, 2008, 2014), Google universal part-of-speech tags (Petrov et al., 2012), and the Interset interlingua for morphosyntactic tagsets (Zeman, 2008). This page lists part-of-speech tags for the 2nd version of Universal Dependencies.