Can there waves in different fields?
Yes. You have already heard about waves in the gravitational field. They were first detected about five years ago!
Waves in the electromagnetic field include light waves, radio waves, microwaves, etc. These electromagnetic waves simply differ in their frequency and wavelength. Otherwise, they are essentially similar because they are all waves in the same EM field and all correspond to the particle called the photon.
Electrons act like waves in an electron field. Quarks act like waves in a quark field. The Higgs particle acts like a wave in the Higgs field.
All quantum particles can act like waves in their respective fields. You can read about wave-particle “duality” here. Physicists discovered that quantum objects can behave like waves or particles, depending on what you do with them!
The Standard Model of particle physics has seventeen different kinds of fields, waves in which correspond to the seventeen known kinds of elementary particles: 6 quarks, 3 charged leptons, 3 neutrinos, 1 photon, 1 gluon, 1 W boson, 1 Z boson, and 1 Higgs. (If you also count different “colors” and antiparticles, you get more than 17, but this is a common way of counting the particles and their fields.)