Salamun Alaikum,
Two terms have been used in 23:6, 'azwajihim' and 'malakat aymanuhum'. Both terms are masculine plurals so there is no exclusive gender reference.
Therefore, 'azwājihim' simply means ‘spouse’. This would include husbands or wives or those married through 'lawful marriage'. The category 'malakat aymanuhum' (right hands possess) would also require ‘lawful marriage’ before intimacy, which is clear from another verse of the Quran (4:25).
The question really is why are 'spouses' and 'right hands possess' mentioned separately as separate categories?
They are not mentioned separately because one category is exempt from lawful marriage. Such an unwarranted assertion would also conflict with 4:25 which makes it absolutely clear that marriage (nikaah) is required with those from the right hands possess.
The reason they are mentioned separately is because in essence they are separate categories (free believers and non-free believers). They also have different ‘accountabilities’. For example, the punishment of 'fahisha' for a married woman from the category of 'right hands possess' is only ‘half’ as that for a free believing married woman (4:25) in the same situation.
I have actually elaborated this in my article in the section entitled
"Why does the Quran distinguish between 'married women' and 'right hands possess' and classify them as separate categories" http://quransmessage.com/articles/sex%20with%20slave%20girls%20FM3.htmI hope that helps, God willing.
Joseph.