What is the difference between the Higgs Boson particle and an electron moving through the Higgs field?

I am watching a lecture by Sean Caroll titled "Particles, Fields, and the Future of Physics". I am not a physicist by any means but enjoy the subject in my spare time hoping to understand it.

This lecture gave rise to a better understanding of quantum field theory for me and how it relates to particle physics.

The first understanding I gained; Carroll mentions that in the view of quantum field theory every particle we know of is basically a perturbation in a field. So an electron is just some "wave" in the electron field. For an electron to "be there" the field itself must be perturbed at that location. (is this correct?)

Another understanding I gained is that these perturbations are energy and that for certain field to be perturbed it takes more or less energy. Specifically that the $W$ boson field takes more energy to be perturbed than the electron field. Even more that if we are given a $W$ boson particle and it decays, its energy can be transferred (by some unknown mechanism?) to both the electron and anti-neutrino fields creating particles of each in that location.

My understanding breaks down when he describes the Higgs field. Specifically that an electron moving through the Higgs Field "gains/is given" mass. Does this mean that the electron is encountering a Higgs boson/particle? Or is it linked to the fact that the Higgs field (forgive me for this butchering of words and physics) is held at a higher energy when not perturbed?

I guess, how is a Higgs particle different from a particle traveling through the Higgs field?

I am pretty sure there could be a good analogue explanation and question between how charged particles experience a force when traveling through an electromagnetic field?

If this question is lack too much understanding, I apologize in advance.

Answer

Yes, an electron is just some wave, as you say, in the electron field, as it is for any particle. You can also interpret in a broad sense that a field needs to be perturbed at a particular point in spacetime for you to have a non-zero odd of measuring it a that point, although this simple picture is complicated by quantum phenomenas.

The energy of a decaying particle not only can but needs to end up somewhere. This is conservation of energy! The mechanism are not unknown, they are the possible interactions (read that as forces) between fields, though they are not all clearly understood in their dynamics.

The idea of billard balls particles colliding is really not the best to have in mind when considering QFT. The electron, which is really a wave/excitation in a field, travelling in spacetime in presence of the Higgs field does not need to ''collide'', in a classical view, with a Higgs particle to interact. Keep in mind that these field excitations are not exactly localized, much as a wave is not. What happens is that the electron field interacts with the Higgs field and as seen form the dynamic of the electron field it corresponds to it having a mass. The closest analogy that comes to mind, which is pretty bad: don't give it too much intellectual weight, is of a bullet going through water that acquires a different dynamic behavior by interacting with the surrounding media, but that's as far as it goes.

Your question about the difference between a Higgs particle and another one, is like asking what is the difference between sound and light. They are not excitations of the same medium.

I am sadly not aware of any good and simple analogies for the Higgs mechanism. The closest thing, which is not simple but quite close conceptually speaking, are electrons in crystal having a different effective mass because of their interaction with the crystal lattice. Without using effective field theories, you can model electron wavefunctions moving in the crystal lattice using standard quantum mechanics. From there, you study their dispersion relation which is in essence the equation relating energy and momentum. The dispersion relation, in some cases, will take the a functional form of a free wave from which you can infer an effective mass. You can interpret that as saying that the interaction with the lattice modifies the mass of the free electron.