SNHU's explanation of the difference between a capstone project and a master's thesis:

"What is the Difference Between a Thesis and a Capstone Project?
Dr. Thomas MacCarty

A capstone is similar to a thesis in that the starting point involves strengths that one needs for a thesis or dissertation work. A student needs to think about the skeletal structure of research and form their theory, hypothesis, and problem statement.

'While a capstone is certainly a scholarly piece of work and does share some aspects of a thesis,' said MacCarty. 'The time and detail that is required of a master’s thesis is greater.'

A capstone paper may be 25 pages, where a thesis could be 100 or more, and is a more demanding research paper. If an undergraduate student chooses to further their education and enter into a doctoral program, the capstone project could be an invaluable tool in preparing for a thesis."

I'd argue that master's thesis is a more accurate translation of the work done in a TFM.
I looked at the proposed structure in subsection 2.2.1 https://www.unk.edu/academics/gradstudies/admissions/grad-fi... and it follows the general structure I had to follow for my Spanish TFM.