Terminological pondering

Is there any term for case-like marking that is neither entirely dependent on dependent- or head-marking? The primary example I am thinking of occurs in my own home dialect, and is a thing I'd like to generalize into the noun morphology of some conlang.

Description of the marking: background facts

In my dialect of Swedish, the separate definite articles behave - as far as the internal working of the noun phrase goes -, syntactically like in standard Swedish: they are optional for noun phrases without adjectives (in fact, having them there when not mandatory is quite marked in standard Swedish; it is slightly less so in my dialect, where the definite suffixes have acquired slightly case-like behaviors in sometimes marking a partitive-like meaning). However, any definite noun with an adjective acquires a separate definite article that is phrase-initial:

bilen <> bi:l`in

den röda bilen <> han rö:d bi:l`in

Now, my dialect retains the old gender system, so modern Swedish 'den' corresponds either to han or hon, he or she. Det corresponds to he. The plural can be ti/tej, and which one of those seems conditioned by intonation and stress patterns - the same distinction exists in both nominative and oblique case first and second person pronouns (ja - ja:g, mi - me:g; tö/dö - tö:g, te - te:g, vi, ve:g - o:s, ni, ne:g - är, edär - but this particular alteration is not what I intend to discuss). Case marking has been lost on the third person pronouns (except hon has an optional dative-accusative, hennar). (Historically, though, han originally did not have an accusative, the modern Swedish honom is a repurposed dative.) 

What distinguishes this system in my dialect from standard Swedish is the presence of another set, tan, ton, te (with no distinct plural forms) exists. This seems to be used frequently when either of these hold:

• there's a restrictive element embedded in the phrase ('the other', 'the one who did so-and-so', "whoever that does this or that ...", "the red one")
• the noun is a restriction in itself, i.e. the answer to a question along the lines of 'which one'? In this case, it often also has a slightly demonstrative meaning, which I don't think it has otherwise.

Using it when none of these are present sounds malformed, although at least I will try to parse it as a demonstrative in that case. 

What kind of a distinction would this be if marked morphologically on the noun? In part it seems to be case-like (i.e. marks the kind of relationship with an adjective or subclause), on the other hand it seems to be something I would not go so far as calling a case.

However, I find this particular thing interesting, and have no idea what to call the kind of category this particular distinction resides in. And what other kinds of distinctions could be made in the same category.