The uke can be set to different "tunings" depending how how you tune the strings. Different tunings will require different chord patterns.
Hold the uke in the playing position. The string closest to your chin is the 4th string. The string closest to the floor is the first string. When people mention string names they go from chin to floor, or 4,3,2,1.
For example:
The D chord on a uke in "C tuning" will be 2220
(4th string 2nd fret, 3nd string 2nd fret, 2nd string 2nd fret, 1st string open)
The D chord on a uke in "D tuning" will be 0003
(4th string open, 3rd string open, 2nd string open, 1st string 3rd fret)
When the strings are tuned to GCEA, this is refered to as "C Tuning". 4th=G, 3rd=C, 2nd=E, 1st=A
When the strings are tuned to ADF#B, this is refered to as "D Tuning". It is a step higher than C tuning. 4th=A, 3rd=D, 2nd=F#, 1st=B
Within each of those tunings you can play songs in different "keys".