A masters or a doctorate thesis is considered a piece of research. It is a considerable and prolonged study of a theory/test of a research question etc. The research question and the sort of data that you will use to explore or test your research question will be what decides your research methodology. That said, researchers do use 'study' and 'research' interchangeably in their conversations. I would consider a study to be a one-stop piece of empirical research - or interrelated sequence of studies on one issue - e.g. a question of health etc. In that sense 'study' is embedded within and can overlap with the term 'research'. Research is a generic term and can describe all research endeavours, but notably it will broadly describe studies and research.
I have attached some useful papers and links below for you to garner an overview of research types and methodologies: