i don't think there is one. I have tuned my ukes using a kala tuner using both settings. Get same results. There might be a technical or theoritcal difference but none that I am aware of.
Is it just that the tuner you're using has a 'chromatic' setting? If so then it just means you can use it to tune to whatever note you want. I assume in C mode it just registers the notes GCEA.
Would it be possible to clarify your question some more? What do you mean by "normal chromatic tuning"?
Tunings (such as D tuning, C tuning, etc.) aren't talked about as being chromatic or non-chromatic. They are simply different ways of tuning the strings on an instrument, and they will require different chord shapes to play chords. The different tunings themselves are chromatic in that they have all the naturals, sharps, and flats in a scale as you go up the fretboard.
Tuners can be chromatic or non-chromatic. A chromatic tuner will be able to register any note on the fly. Non-chromatic tuner registers only certain notes - such as only having the notes found on the guitar (E-A-D-G-B-E). Chromatic tuners let you set your instrument to different tunings because they register all the notes within the pitch range of the tuner (Hz range). Non-chromatic tuners may be set for a specific tuning (C tuning, D tuning, etc.).