"UGC NET" and "CSIR NET" get used interchangeably, and for a mathematics candidate they are not interchangeable at all. Sitting the wrong one is a wasted cycle.
The short answer
If your subject is mathematics, the exam is the Joint CSIR-UGC NET in Mathematical Sciences.
The two tests divide the subjects between them. CSIR NET covers the science streams — Mathematical Sciences, Physical Sciences, Chemical Sciences, Life Sciences and Earth Sciences. UGC NET covers the humanities, social sciences, commerce, education, management and the rest. Mathematics sits on the CSIR side, which is why almost everything written for "NET mathematics" is really about CSIR NET.
Check the current subject list in the official notification before you apply — the split above has been stable for years, but the notification is the authority and subject codes do get revised.
Both are run by the same agency, for the same two outcomes
Both are conducted by the NTA, and both produce the same pair of results: JRF, a funded research fellowship with a higher cut-off, and LS — Lectureship, or Assistant Professor eligibility — with a lower one. A qualification from either is the same kind of credential; what differs is the subject it is in.
If those two outcomes are what you are trying to understand, the eligibility and JRF-versus-LS guide covers them properly.
Where the papers genuinely differ
The structures are not alike, and this is the part worth knowing before you start preparing from the wrong material.
CSIR NET Mathematical Sciences is a single paper in three parts. Part A is general aptitude, Parts B and C are the subject. You may attempt only a fixed number in each part, Parts A and B carry negative marking, and Part C is scored all-or-nothing across multiple correct options. That last rule is unusual and it decides the paper — the exam pattern guide works through what it means for how you attempt it.
UGC NET is two papers — a general paper on teaching and research aptitude, and a subject paper — sat in one session. The marking conventions differ from CSIR's, and so do the attempt rules.
Practice papers written for one are close to useless for the other. A UGC-style subject paper will not train the Part C selection skill, because UGC NET does not have a Part C.
What this means if you are already here
You are on a site about CSIR NET Mathematical Sciences, so you are almost certainly in the right place. The complete syllabus mapped to free video lectures is open without an account, and the previous-year questions carry every option and the correct answer.
Both exams' notifications, subject lists and current rules are published by the NTA. Confirm anything that decides your application against the official bulletin rather than against this page.