Author and public speaker Andrew Solomon describes the differences between sadness and depression very accurately in my opinion. He talks of grief, sadness, and depression, and the differences between these three similar feelings. If you have suffered some catastrophic loss (the death of a loved one, the death of a pet, a breakup, moving to another town, etc.) and you feel deeply sad about it, that feeling is grief. If, after a few months, you are still saddened by your loss, but you can still function in normal day-to-day life and still feel happy at times, then you are typically not depressed, and your grief will ultimately resolve itself given enough time. On the other hand, if after a few months of your loss, you are overwhelmed by feelings of hopelessness, despair, and crippling sadness--so much so that it feels like a struggle just to get through your days--then you are probably experiencing depression that was triggered by your catastrophic loss.
I really like this way of thinking that Andrew Solomon presents. It is totally normal to be sad, unmotivated, and alone sometimes. Even crying for long periods of time is normal--often this just means that you're a sensitive person with a big heart. But if such sadness is affecting you in such a way as to negatively impact all aspects of your life, then your sadness may be depression.
I understand how hard it can be to distinguish the differences between sadness and depression. In everyday language, we tend to use the word "depressed" to describe both a boy that didn't get the toy he wanted on his birthday, and a girl moments before she takes her own life. Granted, these two feelings are related in a way, but they are related rather distantly. It's comparable to the difference between a house with an iron fence that occasionally gathers some rust that the owner has to polish away every now and then, and a house with an iron fence that is left to completely rust over the duration of many decades, such that the fence looks almost nothing like it once was.