I am curious, why does sky130 use different layers for ndiffc, pdiffc, polycont instead of one contact layer? Are those different masks?

is it actually different layers or are you seeing this in magic? Magic uses multiple layers sometimes. @Tim Edwards spoke about this in his recent talk.

AFAIR those are all the same in the GDS, it's just a magic thing.

It's the same except poly contact requires an additional "npc" (nitride poly cut) mask

Magic embeds connectivity rules, so each contact layer is representing the connection between layer1 and layer2. Each of the diffusion and poly contacts ultimately results in the output of the same contact cut type in GDS. But there are additional layers, as each contact type will also output the layers on top and bottom, as well as N+ or P+ for diffusions, and the NPC layer for poly as Matt mentioned. By using a separate type for each context, it is also much easier to specify the separate DRC rules for poly contacts vs. diffusion contacts vs. tap contacts.