The two words are similar. In practice, I think that the word tipped is applied more to inanimate things. So I don't think that you would say "tipped her head", that would always be "tilted her head". The other two sentences could use the word interchangeably. I am not sure that I am correct but as a native English speaker, I feel that "tipped" is associated strongly with "tipped over" indicating some sort of accident rather than a planned movement.

They're very close in meaning. I think the first and last examples could be used with 'tilt' - possibly not the second. With the glass of water example, 'tip' could be the idea of 'tipped right over onto the table' ie knocked down entirely, which is different from 'tilt'. 'Tilt' suggests a leaning/change of angle on one axis only, whereas 'tip' , I think, is a less precise movement. Consider the word 'tipsy', for example, meaning slightly drunk (a bit 'wobbly').