You've actually got it pretty accurately, shelyksit. It does get a bit confusing with multiple (and often changing) terminology. Pulse is the feeling of movement in time in its simplest form, and in a certain meter (time signature/way of counting). Rhythm can be, and is, played by any instrument, but what we often think of as the main rhythm of a song is usually played by the drums, sometimes the drums and bass (also known as "the groove"). A lot of folks call this the beat (which in itself is a musical misnomer, and that's been made even more confusing now that almost everybody, since the 90's at least, calls instrumental musical tracks "beats").
So, "the beat" is played by drums and other rhythm section instruments, with a certain pulse (overall rhythmic feel that can be counted a certain way, called meter), which is at a certain tempo (or speed, measured in BPM, or Beats Per Minute). And this is _all_ rhythm, as any instrument that plays notes in succession of varying lengths and in repeating patterns can play rhythms, but the main rhythm is the one we call the groove. But where you bob your head is actually more properly called the pulse. Clear as mud???
GJ