If a nomic and causal relation is a relation in which something cause something else and this effect is dependent on the properties of the causal object, what is specific in a simple causal relation?
"Nomic" usually makes reference to the fact that there is a natural law, or some weaker form of lawlike regularity, which is exemplified by the relata of that episode of causation. The throwing of the stone and the breaking of the glass are like that (ceteris paribus, defeasibly, but robustly, etc. if a stone is thrown to a glass with the requisite force, the glass will break.)
I suppose it is possible to think of causation in the absence of this lawlike component. For example, depending on how you develop the notion of nomicity, it is possible that selection for a certain trait in a population, in a certain ecological niche, is not covered by any such lawlike regularity. But it will still be causal.
As referenced in your link, due to Hume's first 3 criterions to establish causality:
- "The cause and effect must be contiguous in space and time."
- "The cause must be prior to the effect."
- "There must be a constant union betwixt the cause and effect. 'Tis chiefly this quality, that constitutes the relation."
A singular (simple) causality just needs to satisfy 1 & 2, while a nomic causality has to satisfy 3 further to bear some at least probabilistic general laws.
For example, every time you see your car a fear is immediately felt (only by you) since maybe you had an unforgettable accident with this car before and it made a long-lasting impression only to you. So "you seeing your car then fear arose in you" is a singular causal relation, but not a nomic one due to no such general law exists applicable for most people when they see their cars.