I don't know whether it's the same as human-style grief and depression, but cats can certainly show signs of depression and grieving.
In my experience, cats who lose a close companion cat can show signs of grieving such as:
- searching the house for the missing companion cat and calling for them.
- demanding much more attention from their human companion(s).
- change in eating patterns (not eating/overeating) - in my experience this doesn't last long.
- inappropriate urination and defecation (this is also an anxiety response - but I've seen it happen in response to a cat losing a close companion cat)
- spraying (I've usually seen this happen when a companion cat is dying rather than after they die, and it's probably more related to claiming the territory from the dying/dead cat than anything else - but it sure doesn't help matters, particularly when the cat doing it is obviously trying to get your attention (I've seen this happen: cat walks into room with humans. Backs up to curtain. Sprays. Watches humans the whole time. This was a neutered male...)
Whether the behavior changes indicate the cat is depressed or not could be argued endlessly, since we can't tell how much is anthropomorphism and how much is the cat's natural response to the loss of a close companion. In my view, it's close enough to count.