There are two different systems at work in the citations of (Runge and Levinsohn) versus (Larsen).
Larsen has a simple scaler: the more to the left the more prominent.
Runge, Levinsohn, H. Dik, S. Dik, myself, and many functional linguists differentiate fronted constituents as Topical/Contextualizing vs Focal.
If the left-placed constituent is the most salient piece of information, then it is called "Focus" (or synonym), while a left-placed item that is not the most salient (important, reason for statement of the clause) is viewed as marked for contextual/relational reasons, to set up a topic/context span, name an entity for comparison/contrast, break the default foregrounded chaining.
The differentiated, multi-reason is the majority view in linguistics. In terms of signal, it is assumed that left-placed constitutents will also interact with the intonation/tonal system of a language so that a differentiated signal is possible in a language for a left-placed item.
Of course, this does not answer all questions for readers where texts do not have intonational/stress/tone differences marked in a text. The reader must supply their own reading and interpret left-placed constituents as either normal-left-placed (contextualizing contstituents) or marked left-placed (focus constituents).
[PS: a constituent may be more than one word, a whole phrase, or sometimes a partial constituent, a word from a phrase.)