That page is actually a little out of date, sorry about that.
The basic principles still apply, but there are a few nuances.
Essentially, the system is:
sutta_number:section_number.segment_number
And most texts are like this.
However, in certain cases, notably dn and the Vinaya, we endeavored to keep our section numbers in line with the previously-published section numbers of the PTS editions. So what happened was that the PTS published certain texts with section numbers, but they didn’t do it for all texts, and people ended up not really using them and just using volume page instead. I think this is a big missed opportunity!
I didn’t want to unnecessarily impose a new section system where one already existed. So we made the decision to respect the pre-existing section numbers for dn and vinaya; and also Nyanamoli’s numbers for mn, but these don’t get into the extra level.
The cases where there are more deeply nested numbers are usually those places where the PTS edition used such systems. Maybe this was a mistake, maybe we should have just kept the three-part number throughout, but oh well!
So dn1:1.10.3 is section 1.10 in the PTS edition, segment three.
The situation with thag is different, there the numbers merely distinguish a heading and homage section that precede the first verse. For these, we use zeroth-level numbering, and it’s just an unusual case that required an extra level. Similarly in mn10, it’s caused by the nested heading structure, otherwise they all have the normal form.
We usually just use “sutta” for everything, or maybe “text” if we’re being inclusive. There’s no specific term for “individual Vinaya unit”.