Someone can suffer from or have anxiety, depression or stress. The choice of one of those verbs or the other can determine whether one is talking about a medical condition or not. However, sometimes it’s have that makes it sound medical, and sometimes it’s suffer from that does, so it’s hard for me to explain when to use one or the other.
The three words are not synonymous.
I understand anxiety as being a kind of low-grade fear, but it doesn’t always involve stress. I suppose this is why you can frequently hear the phrase stress and anxiety.
Stress, to me, is a lot of emotional tension. You can have stress without any anxiety or depression. For example, some people get high on the stress of project deadlines or the stress of trying to win a sports match.
Depression is more like enduring sadness that doesn’t change from hour to hour or day to day. You can have depression without any stress or anxiety.