Anxiety is not a "normal" state of mind, it is an irrational fear or worry about something that is not likely to happen.
Depression is also not a "normal" state of mind, often (but not always) viewing the world in a negative way when there may indeed be nothing to be "depressed" about.
So I would say the two states of mind are linked.
As it says on Wikipedia
Anxiety is an unpleasant state of inner turmoil, often accompanied by nervous behavior, such as pacing back and forth, somatic complaints and rumination. It is the subjectively unpleasant feelings of dread over something unlikely to happen, such as the feeling of imminent death.[