What is the differance between a 12 hole and 10 hole ocarina?

The difference between a 10 hole and 12 hole ocarina on the surface is minor, but there are some notable differences with regard to playing characteristics.

10 hole ocarinas have 10 finger holes, 8 on top for the fingers, and two thumb holes. They look something like this:

Two Italian ocarinas, each shaped like a long cone. One is in C, the other G, and both have 8 visible finger holes of varying size.

A 10 hole ocarina plays chromatically over a range of an octave and a fourth, for example C to F.

A 12 hole ocarina is essentially the same, the only difference being the addition of two 'subholes'. They extend the low range downwards by 3 semitones. Thus a 12 hole C ocarina would have a playing range from A to F.

A diagram of a 12 hole ocarina depicting the subholes. Subholes are small additional finger holes placed besides other holes. They are used by covering 2 holes with one finger, and allow lower notes to be played.

The fingering system of 10 and 12 hole ocarinas is almost identical, and if you learn either you will be able to play the other kind with only minor adjustments.

The differences between 10 and 12 hole ocarinas become apparent when considering their playing characteristics.

Playing characteristics of 10 hole ocarinas

Due to the physics of the instrument, having a smaller range allows 10 hole ocarinas to have a strong, clean sound through the whole range.

There is a lot of freedom to craft the playing characteristics of a 10 hole ocarina, and they may:

Play at low breath pressure, with a balanced volume through the whole playing range.
Play at high pressure, sounding very loud throughout the entire range.
Play with increasing breath pressure, having quiet low notes and loud high notes.

They can also attain quite a range of timbres from 'pure' to 'reedy'. All of these things are set when the instrument is made. But despite their flexibility, as of writing few makers are exploring that possibility space.

Playing characteristics of 12 hole ocarinas

The extended range of a 12 hole ocarina puts far more constraints on their design, and due to this there is much less variation between them:

12 hole ocarinas play with a steep pressure curve, having quiet low notes and loud high notes.
They often have imbalanced timbre over their range, with airy sounding high notes, and weak low notes.

It is worth noting however that ocarinas do not scale linearly. A 12 hole soprano C can easily play cleanly over its entire range, while an alto usually exhibits some of the issues noted above. 12 hole bass ocarinas are even more problematic.

These factors are discussed in How ocarinas work.

The 11 hole ocarina

It is worth mentioning that a middle ground exists. The 11 hole ocarina is a compromise between the 10 hole, and 12 hole designs. They have one subhole which can be placed on either the left or right hand.

11 hole ocarinas have one subhole, normally positioned on the right hand middle finger. They can play one semitone below the tonic note.

By eliminating one of the subholes they retain most of the design flexibility that a 10 hole ocarina allows. The timbre and volume of the whole instrument can be balanced.

But providing one subhole allows a semitone below the instrument's base note to be played, which is useful in a lot of music.