There are four common sizes of uke. From the smallest down (in pitch):
All but the baritone are commonly tuned in a reentrant tuning. However non-reentrant tunings for all four also exist, and also slack-key open tunings. Generally, the larger the uke, the more likely it is to be tuned non-reentrant.
The most common size and standard student instrument.
Standard tuning is C tuning (reentrant), also know as high-G or high-4th tuning:
Also common is the slightly brighter D tuning:
Non-reentrant D tuning is known as Canadian tuning:
Non-reentrant C tuning is known as low-G tuning or low-4th tuning:
Just two common tunings, high or low 4th, also known as high or low G, respectively:
Yes, these are just the two C tunings for the smaller Soprano! The Concert is just louder and more full-bodied than the Sop, and less suited to D tunings.
Low-4th:
High-4th:
D tuning:
Canadian:
Rarely tuned to anything other than non-reentrant: