How come doing bodyweight exercises “tone” the body, but lifeing weight doesn't?

but aren't they both just “weights”? what's the difference between the two?

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Answer:
Without getting too technical
“tone” is not a physiological term… it's just a word people use when they don't want to state 'build muscle'. It's very often used with women. Most women don't want to 'build muscle' because they are afraid of getting too large so they say “tone”

Any kind of resistance training (weights, body weight, dumbbells, barbells, bands, etc) produce a training stimulus. The body will respond to this stimulus by getting stronger and building muscle, how much strength or muscle varies HUGELY depending on individual circumstances.