Is the electroweak force similar in behavior to electromagnetism and the weak force or is it completely different? Does the electroweak force govern particles in a similar manner to the electromagnetic and weak forces, and is therefore just an easy label or does it do something completely different? Also since it's a combination of two forces, does one force give rise to the other similar to how electricity gives rise to magnetism and vice versa?
 A: All of the above; there is never an exclusive "or" there.

*

*"Electroweak" describes the umbrella theory of the Standard Model which links and fuses electromagnetic and weak interactions at short distances. (At long distances, only electromagnetism survives, and decouples from the rest.) At shorter distances, novel phenomena like Higgs interactions emerge, so you might argue something qualitatively different is taking place, but "completely" is, of course,  a meaningless unwarranted logical dichotomy.


*The two forces are "joined at the hip" and fit together nicely, but there is no obvious way to derive one from the other through a transformation similar to the Lorentz boost. You are probably belatedly victimized by the glib analogy that unthinking and misinformed science writers of the 1970s chose to toss around, to confuse their defenseless and impressionable audience. (In all fairness, even Weinberg himself, at the time, used that glib parallel to Maxwell's unifying linkage of electricity with magnetism.)


*In reality, there are two gauge theories brought together and "weak-mixed" in a characteristic way discovered by Glashow, nowadays called "Weinberg angle mixing", the resulting pieces being the long-range electromagnetism familiar from the past, and the short-range weak interactions. Both of these pieces part-take in both  the underlying gauge theories, and the resulting mathematical fit works quite well in describing a huge number of processes, probably all known ones.
