A tone doesn't need to have a musical reason for being. It can simply be a beep coming from an electronic gadget, for example, or a bell being rung. It's any sound which has a discernible fundamental and/or overtones.
Probably one would not define a burst of white noise to be a “"tone”, although some with more liberal definitions might disagree. This is because there's no discernible pitch in white noise. Same with, say, a slap in the face or the sound of food frying; those are largely inharmonic sounds without a discernible pitch. Those events I would call “sounds”, whereas a tone usually is associated with a pitch or pitches, or a sound that has at least a nominal degree of periodicity. So tones are a therefore a subset of all sounds.
A note, however, is a subset of tones. Notes are tones which have been given a musical context, and which fit within a framework of defined pitches in a musical scale. Actually at its essence, a note doesn't even have to be manifested physically - it can just be a theoretical construct on paper or heard in the mind’s ear. A tone just has a wider range of applications than purely musical ones.
A tone can of course also be a note, once the tone is given a reason to exist musically, and provided it has a steady enough pitch to be classified as a note. It's only musical context that provides for defining anything as a note.
So in sum: (in the physical world) a note is always a tone, but a tone isn't always a note.