Throughout my life I have oscillated between the two. I always had social anxiety - though in my day it was just known as shyness. I also always had mild depression. When I became seriously ill in 2015 the two things seemed to merge together to create a monster. As I mentioned before, I actually experience my depression as anxiety. I have a tightness in the chest and a semi-permanent headache. And I simply can't relax. No matter how much deep breathing I do or how much mindfulness or vizualisation - the sense of dread/panic remains. My depression was of the agitated variety - so maybe this explains the similarities with anxiety. Some days I wonder if it is actually more anxiety than depression. After all, anxiety is a key cause of dizziness. Anxiety also causes a tape-loop of thoughts - not dissimilar from rumination.
The treatments for anxiety and depression can also be interchangeable. Strangely, antidepressants are often prescribed for people with anxiety. Mindfulness can be effective for both illnesses. Being calm is also a way of combating both.
Sometimes I find it's helpful not to compartmentalise the two illnesses. Just try and deal with how it feels.