In science, a hypothesis was a tentative conjecture for explaining an observation, a phenomenon, or a scientific problem. The hypothesis was tested by further observation, investigation, and/or experimentation. A hypothetical was a conjectured statement, situation, or question about something imaginary.
In 2268, Spock extracted the salient portion of Professor Starnes' microtapes which contained, according to Spock, some rather unscientific hypotheses. (TOS: "And the Children Shall Lead")
In the T'Kal-in-ket, an ancient philosophical process on Ni'Var, the challenger had to vigorously defend their hypothesis before a Quorum. (DIS: "Unification III")
In 2368, Berlinghoff Rasmussen was unwilling to influence Captain Jean-Luc Picard who was faced with the dilemma of the planet Penthara IV slowly turning to ice which would result in thousands, maybe tens of thousands of deaths, in a matter of weeks. Rasmussen began to ask a hypothetical about the possibility of a person growing up to be, as Picard put it, the next Adolf Hitler or Khan Singh, but Picard shouted that the situation was not theoretical or hypothetical, it was real. (TNG: "A Matter Of Time")