The Church is very clear on not giving holy communion to cohabitators, I guess its mainly because they are living like married couples (having sex outside the bond of marriage). Fornicators do the same thing, they have sex before marriage and surprisingly the church are not strict with them.
Sex outside of marital covenant is by matter, will, and knowledge - a mortal sin. Both person’s who have not confessed their sins, and do not repent, cannot therefore receive Holy Communion.
But, let’s suppose we take one person, a fornicator. And then another,who co-habitates. Generally, The fornicator, if he or she goes to Confession, declares their sins, and repents, and therefore receives Absolution. He or she can then receive Holy Communion.
When someone who co-habitates, goes to Confession, declares all their sins, repents, and receives Absolution. They also can receive Holy Communion.
I don’t think the process is different. However, I think the perception is much harder for someone who co-habitates can see their sins, as apart from a person who fornicates. For, the co-habitant considers his or her state like it were marriage. Because, they love each other. Wherefore, the fornicator - which is quite obvious - generally sleeps for a hookup/one night stand. And so it is easier/more obvious to tell someone who is fornicating what they’re doing is wrong. But with someone who co-habitates, it is much harder to convince them that what they are are doing (if and only if they are sleeping with this person as opposed to a morally chaste life), then it is much harder to tell them they are in mortal sin.
The Church puts harsher rules, maybe (because I haven’t really read much, but only from what your post says) to make the co-habitants fully aware they are in mortal sin. And the measure of penance for them to be reconciled is much greater a burden because they lack the eye site of their souls to realize they are in mortal sin. Whereas a fornicator, it’s much quite easier as they don’t really believe they love the person they are having a one night stand with.