C3 on the keyboard
C3 is one key on a keyboard.
C3 is one key on the keyboard, and no other key sounds that pitch. The coloured keys are the other Cs, each in a different octave.
C3 on the neck
C3 lies at on ukulele — low g (gcea).
C3 lies outside this instrument's range. The faint notes are every C it can reach.
On a piano, middle C is one key and there is nowhere else to look. On a ukulele, most notes in the middle of the range can be played in two or three places, and a few in four. Each place gives the same pitch and the same name, but feels completely different under your hand.
This is what makes a fretboard feel hard to learn at first, and it is also what makes it worth learning. A guitar often offers four or five places for the same note. Four strings offer fewer, which makes the choice easier, although it is still a real choice.
The diagram marks one pitch on the keyboard and lights every place it can be played on the neck. The places are not interchangeable, because only one of them may leave your other fingers within reach of the next notes.