I don't know if there is any difference between the two, perhaps in how they may react to the depression in their every day life. Since I really don't know much about how depression may affect personality type, specifically Fi vs Fe, I can only offer my own experience with bouts of depression. I think that normally I have a fairly good use of my Fe. I am an Ni-Fe user (I think), so not my strongest function, but in there.
Trying to go with what relates to my Fe alone, when I begin to struggle with depression, I also start to withdraw from people, and I can't handle other peoples' emotions for them. In a way, I am very much aware of other peoples' feelings and I absorb them, and feel in part responsible for them, so it can drive me crazy and this is why I need to withdraw so much, because I can't handle it any more and the only way to free myself of that extra burden is to separate myself from others, since I can't shut it out very easily as long as I am around them. I am not very in tuned to my own feelings and emotions on the other hand, so I often don't realize I am depressed right away until it is bad.
In a way, I also do not have a strong self identity, since I am not so in tuned to my own feelings, so when I begin struggling with depression, I also become a bit dissasociative and detached. For a time I thought I was INTP, since I thought I was using Ti quite a bit, but I think I get into Ni-Ti loops, which might stem from my bouts of depression and withdrawing into my introverted functions. With different levels of depression I have different levels of reaction and such, at times being more apathetic, other times more gloomy and sad, or struggling with anger.
Because of my Fe, I have always by nature been very friendly and engaging with in-person communication (outside of family), so even when depressed, I am this way, though it wears me out, thus the reason I withdraw. But really, all these things can happen to anyone with depression.
Basically:
I withdraw.
I become listless.
I can't handle others feelings.
I struggle to take care of others.
I can't take care of myself.
I give up on people and friendships.
I only speak from my own personal experience, and I am also not completely certain of my own personality type, so I could be wrong on that too in some of my explanations regarding my reactions. Also, I have never been clinically diagnosed with depression, though I have had other health issues (non-mental), which have resulted in my depression bouts.