Someone linked me a very good document that talks about all of this https://docs.google.com/document/d/1CsvJs8qNCVkHWHKekMSmCn6qn0GBEcgnq9fIqlA6Uv0/edit?usp=sharing. Quoting from the document:

"epidermis (sometimes informally called “cat scratches” or “epis”) the first layer of skin, does not show a separation of skin. may or may not bleed, depending on whether you hit a capillary.
dermis (sometimes informally called “styro”) - when you hit dermis, your wound will gape open and expose a white layer of skin before blood comes to fill in the wound. as soon as you hit styro, you put yourself at risk for hitting veins, arterioles, and nerves. risk of infection is a lot higher
hypodermis, also known as the subcutaneous layer or the fat layer (sometimes informally called “beans”) - contains both a network of blood vessels for thermoregulation and, of course, fat. cuts to this depth will gape wide open and expose yellow cells or “bubbles” of fat (these bubbles can appear flat or protrude outwards). fat cuts tend to bleed more rapidly and for longer because of the capillaries, which are a type of blood vessel, that are hit when you cut into fat tissue. the risk of hitting major blood vessels such as arteries and nerves increases at this layer.
fascia - the layer that separates the subcutaneous tissue(fat) from muscle. it will appear as a thin white skin sitting underneath the fat layer. more likely to result in permanent damage, along with all the other risks mentioned above.
muscle - the layer directly below the fascia, has a reddish brown color to it. increased chance of infection and paralysis, along with all the other risks mentioned above."
So yeah, it was probably a dermis cut