Ocarina naming conventions
Ocarinas are usually classified both by the number of finger holes and by the number of chambers. The common basis of the single chamber is Guiseppe Donati’s 10 hole design consisting of 8 finger holes and 2 thumb holes, typically called a 10 hole ocarina.
Single chamber ocarinas often have more than these 10 base holes through the addition of subholes and split holes.
A subhole is an additional hole placed besides one of the 10 base holes, and covering them extends the range of an ocarina downwards. If they are ignored, an ocarina with subholes plays the same as one without. An example of a subhole is shown in the following picture.
Ocarinas can have one or two subholes added, and such an instrument is called an 11 hole or 12 hole ocarina. Note that more holes isn't necessarily better, as covered at the end of the page.
Split holes look similar to a subhole but serve a different function. They do not increase the sounding range, but are a single hole that would normally produce a whole tone, that has been split into two to make an accidental (sharp or flat) easier to play.
The chromatic notes of an ocarina are played by 'cross fingering', covering the existing holes in a different order. On the high notes, this produces a well tuned accidental as there are many possible combinations. The number of options available decreases towards lower notes, and the available holes don't always allow a well tuned accidental. A split hole addresses this by giving the accidental a dedicated hole.
Note that the presence of a split hole does not change how an ocarina is named: while an 11 hole ocarina with a split hole technically has '12 holes' in the sense of having 12 holes to be covered by the fingers, it is still an 11 hole ocarina in naming and practice. You can think of a split hole as two .5 holes, together counting as a single hole. This is done because strictly using hole count as a classifier would be ambiguous, as the holes can serve differing functions.
Classifying ocarinas by hole count is also problematic as ocarinas can be tuned in different ways. This may be done to make playing music from a given tradition easier, such as the Lydian soprano G I make for Highland pipe music. Non-Western scales are also possible, and naming using hole counts reveals nothing about these differences. In such cases, it is important to look for additional descriptions or a fingering chart.
Multichamber ocarinas are sometimes classified using hole count, but doing so is often ambiguous. Multichambers from different makers often have variations in their hole counts and fingerings. Higher chambers may have subholes, and there are two different tuning systems in use, Asian and Pacchioni.
Instead, they are classified relative to the number of chambers. Doubles have 2 chambers. Triples and quads have 3 and 4 chambers respectively. Thus, you will often see an ocarina classified as 'Double ocarina, Pacchioni system'. The Asian system is rarely mentioned as it is more common and essentially default.
Knowing the exact fingerings for any single multichamber ocarina requires reference to a fingering chart. See 'Multichamber ocarinas and their tuning systems' and 'The fingering systems of multichamber ocarinas'.
Variations in playing characteristics
Even within one of these groupings, ocarinas can vary a great deal. Varying factors like chamber volume, voicing size, and tuning, plus other factors like the size and smoothness of the windway, results in differing playing characteristics and timbre (tone colour).
For example, traditional Italian ocarina designs trade off some range to attain maximum volume, using a very large voicing, an open windway, and high pressure. The 12 hole design on the other hand uses a (typically) lower pressure, smaller voicing, and smaller chamber volume, reducing airstream turbulence and allowing a larger range to be attained.
Many variations in volume, and timbre are possible, varying from a very pure sound, a 'reedy' sound, or a loose, airy sound. But of these, only designs leaning strongly towards a pure sound can provide the full range of a 12 hole. Thus, more holes isn't universally 'better'. These issues are covered on the page 'Ocarina playing characteristics and timbre'.