In the Jewish way of numbering the 10 commandments, all the "do not covets" are part of the same commandment (that is, the 10th commandment.) However, in the text there is a stuma break between coveting another's wife and coveting another's possessions. This would seem to suggest they are separate in some ways. Have rabbinical commentaries said anything about why the stuma break is there? Or about why we number it the way we do despite the stuma break?
This is a concern specifically in the version of the Aseret HaDibrot in Devarim 5 (Parshat Vaetchanan), and not in the version found in Shemot 20 (Parshat Yitro).
In Yitro, there is no break between the different sections of 'Do not covet'. There is also no parsha break between "I am the Lord your G-d..." (verse 2) and "You shall have no other gods" (verse 3-6). Otherwise there are parsha breaks between each of of the 'dibrot', including those found in a single verse (verse 13). So here there are only 9 parshiot and a desire for 10 Dibrot.
In Vaetchanan, there is a stuma break within verse 18, as you note. The parsha breaks are otherwise the same, in that "I am the Lord" and "You shall have no other" are in a single parsha. This creates 10 parshiot and 10 Dibrot. These line up with what I think of as the Christian ordering, though there may be Jewish sources that count this way, where the first commandment/dibra includes both "I am the Lord..." and "You shall have no other...", the Ninth is not to covet a wife and the 10th not to covet other things. The other dibrot are not disputed that I am aware of beyond the count changing if "You shall have no other" is the second or part of the first.
Counting this way fits the Devarim section better in that it fits with parsha breaks. However, it creates problems in the Shemot text as then Shemot (seemingly the primary place for mentioning the Aseret HaDibrot) mixes not coveting wives into the middle of not coveting possessions. It also creates a problem with the derivation late in Makkot that there are 613 mitzvot. That relies on there being 2 mitzvot in the section that was taught directly by G-d, and that section is presumably where G-d speaks in first person rather than in third person. That shift occurs between "You shall have no other G-d's before Me..." and "Do not take the Lord's name in vain". One could claim even if it is one dibra that it contains two mitzvot, just as there are mitzvah counters who do not count Anochi as a mitzvah even though they do count it as a dibra.