Although there is a case for closing this question (it is two questions, the first of which is more linguistics, logic or philosophy of science, and the second well-covered in text books) I have chosen to answer it, mainly because neither of the terms hypothesis or theory describe the current status of the proposal (the neutral description I shall employ initially). I have restructured my original answer putting the science first, and providing more information on this.
As the title of his original 1961 Nature paper makes clear (“Coupling of phosphorylation to electron and hydrogen transfer by a chemi-osmotic type of mechanism”) Mitchell was addressing the following question: How is the free energy released from the electron transport chain — involved in the oxidation of NADH and FADH2 by oxygen — used to phosphorylate ADP to ATP.
At that time it was assumed that this was by a mechanism in which the energy was used to generate a chemical compound, X~P, containing a phosphate bond with a high free energy of hydrolysis, which could be used to phosphorylate ADP to ATP. (This was influenced by the ‘substrate-level’ phosphorylation occurring in glycolysis.) In brief, Mitchell proposed that the phosphorylation did not involve any compound, X~P, but was catalysed by an ATP synthase enzyme powered by an electrical gradient, established across the membrane in which the electron transport chain resided.
Mitchell proposed a possible mechanism for oxidative phosphorylation in terms of conventional physics and chemistry. Just as the postulated X~P, had not been identified, neither had the components of his proposed chemi-osmotic mechanism. The paper focused on its quantitative feasibility (making it challenging reading for many biological scientists), although it did also argue that the idea was consistent with a series of experimental observations that were difficult to explain in terms of substrate-level phosphorylation.
It was a hypothesis
Regardless of the interpretation of dictionary definitions, considered below, it was a hypothesis because that was the word Mitchell used in the original paper, cited above, a paper in which the word theory does not occur.
As well as misquoting history, it would seem presumptuous to use different terms to refer to the proposal of the original author, a proposal which resulted in his award of the Nobel Prize.
It is a fact
The mechanism of oxidative phosphorylation has now been explored in great detail and the general features of Mitchell’s hypothesis have been generally validated. It can be considered as much a fact as any other in our general conception of cellular biochemistry.
The famous experiment that resulted in widespread acceptance of the hypothesis was the so-called acid-bath experiment of Uribe and Jagendorf. In this experiment ATP was generated in the dark and without electron transport by loading the inner space of the grana disk membranes of spinach chloroplasts with protons.
More recently the structures of all the proteins involved in the chemiosmotic mechanism have now been determined, including that of the ATP synthase, the molecular machine which uses the electrochemical gradient to phosphorylate ADP to ATP. and the components of the electron transport chain.
Merriam–Webster, on-line, is quite dogmatic about the difference between the words hypothesis and theory:
A hypothesis is an assumption made before any research has been done.
It is formed so that it can be tested to see if it might be true. A
theory is a principle formed to explain the things already shown in
data. Because of the rigors of experiment and control, it is much more
likely that a theory will be true than a hypothesis.
But is this dogmatism justified, and how does it apply to the current problem? Mitchell’s proposal was made to be tested (as in a hypothesis) but it was intended to explain the observed phenomenon (as in a theory) of oxidative phosphorylation.
An extensive article in Wikipedia begins with a more modest statement:
A hypothesis (plural hypotheses) is a proposed explanation for a
And chemi-osmosis is a proposed explanation for the phenomenon of ATP synthesis in double-membrane systems; so by this token Mitchell’s choice of words seems justified.
Major dictionaries record how words are or were used in practice. In some contexts there are sharp distinctions in usage of particular words, where in others the same words are used interchangeably. In modern biological science, unlike philosophy, logic or the numerical sciences, laws, theories and hypotheses are generally of no great concern, and the writers quoted may merely feel that the word ‘theory’ (‘Einstein’s’ theory, ‘Darwin’s theory’) has more gravitas than ‘hypothesis’, a word they perhaps use to describe ideas about relatively humble scientific problems of their own.
…or they may just find it easier to spell.