Other answers pointed out that the amount of support for PhD students (post-qualifying exam) can be higher than M.S. students. However, in addition to funding levels, funding sources for PhD and M.S. students can be very different.
For example, in my lab (US, engineering), most of the M.S. students working as research assistants are supported by funds allocated by the department to the professor every semester. This money is given specifically for the purpose of creating extra educational and training opportunities for M.S. students, through participation in research.
Then, in my lab, the funds that support PhD students usually come from their advisors' research grants. (A small number of PhD students are funded by the department for a year, but this comes from a very limited "pool" that is separate from the M.S. student money, comes directly from the dept to the PhD student - not the professor - and is much harder to get. Some PhD students are funded by external fellowships, like NSF Graduate Research Fellowships.)
You didn't ask about undergraduate researchers, but we also have those in my lab, and they are often funded by the NSF from Research Experience for Undergraduates (REU) grants.
Thus, in my lab there are certain funds that may be used only for undergrads (from NSF via REU grants); certain funds that can go only to M.S. students (from the department, via a pool of money allocated to create research opportunities for M.S. students); and certain funds that can go only to PhD students (from the department, via a pool of money allocated specifically for one-year PhD fellowships). Then there are funds (mainly, from the professor's research grants) that can be used to support any kind of student.
This is of course just an example - other labs will have entirely different "pools" of funds that they may draw from, which may or may not have restrictions as to who may use them.
It is entirely possible for a professor to be able to fund an M.S. student (because it comes out of departmental M.S. research opportunities money) and not a PhD student (because they don't have enough active research grants, or all their grant money is already committed, and the department PhD fellowship pool is empty).