I think it is inappropriate to compare depression to the flu.

Depression is a chronic illness, the flu is temporary.
Something like diabetes, kidney dysfunction, severe allergies, epilepsy etc would be a more appropriate comparison.

Having a chronic illness or health complication, mental or physical does change how you perceive yourself.

I imagine that you might possibly have little to no experience with serious chronic physical conditions. It is much the same as having a mental illness: you feel you are limited by your condition, you get constant criticism, you continually look for treatments that will work long term, you deal with crap resulting from the condition pretty much every day.

Constant maintenance, frustration, understanding of limitations, eschewing others' impression of what your limits SHOULD be [as opposed to what they are]...

It's very similar.

I would encourage you to talk to any individual who has personal experience with any one of the following:
diabetes, cancer, chronic fatigue, fibromyalgia, moderate to severe asthma, epilepsy, immune system disorders/severe allergies

[I have the last three as well as MI issues- I speak from experience and am qualified to make this comparison. I also have many friends who experience these issues as well.]

I think it is easy to see the differences because sometimes it feels like our situation is so damn hard that no one can possibly relate.

There are more similarities between the differing situations than one might think.