A via, also known as a contact, connects two layers together.

Staggered via: when connecting through multiple layers sometimes its preferable to not put all of the vias vertical but instead offset them

Stacked via: connecting multiple layers together by putting all vias directly on top of each other

Pads are not considered vias as they don't connect two layers together in the IC.

Through-silicon via (TSV): http://www.ece.ncsu.edu/asic/ece733/2013/docs/3DIC_12_Franzon_tutorial.pdf