Relativity theory fits well into this description. It (the special relativity) was derived from a formal attempt to unify classical mechanics and Maxwell electrodynamics, which was only possible if you ditch the Galilean relativity. Both classical mechanics and electrodynamics, in turn, came from a huge body of experimental data.
General relativity is a different thing, it was a pure hypothesis, an extrapolation of the simplest possible generalisation of the special relativity [1]. And it held this hypothesis status up until it was sufficiently confirmed by the incoming experimental data. Before that, a multitude of alternative hypotheses existed which had the same numerical predictions covering the available experimental data (e.g., https://en.wikipedia.org/wiki/Anatoly_Logunov#Relativistic_t...).
So, yes, it's important to distinguish theory from a hypothesis.
[1] this "simplest possible generalisation" method works most of the time, but not always, so it's mostly valid to do so in the hard sciences, and should never be used as a justification for hand waving in the social sciences.
General relativity is a different thing, it was a pure hypothesis, an extrapolation of the simplest possible generalisation of the special relativity [1]. And it held this hypothesis status up until it was sufficiently confirmed by the incoming experimental data. Before that, a multitude of alternative hypotheses existed which had the same numerical predictions covering the available experimental data (e.g., https://en.wikipedia.org/wiki/Anatoly_Logunov#Relativistic_t...).
So, yes, it's important to distinguish theory from a hypothesis.
[1] this "simplest possible generalisation" method works most of the time, but not always, so it's mostly valid to do so in the hard sciences, and should never be used as a justification for hand waving in the social sciences.