Well, for one thing you are asking about a photodiode, and showing an image of a photocell (same thing as a solar cell, though usually much smaller); strangely, though, the highlighted portion in the schematic seems to be indicating resistance of the photocell (dark vs. light resistance, or vice-versa) - which I usually associate with cadmium sulphide cells/photoresistors/LDRs; but I suppose a photocell can have a resistance, too.
As far as what a photodiode looks like - I have seen all kinds; some are nearly "bare", some look like LEDs, some look like transistors (ie, in a TO-92 case, sometimes a clear case, etc). If you have a device and don't know what it is, I am not sure how you can tell. I mean, a regular transistor, and a photodiode/phototransistor in a similar case are easy to tell apart, because the light sensitive version will have a clear window or plastic to admit light to the junction.
But then again, I have in one of my drawers a device that was mixed up in with a bunch of phototransistors that looks like a very small (size of a grain of sand, actually) axial lead LED! I have no clue what it actually is, although the fact that it was in a small plastic box with a bunch of old phototransistors indicates to me that it to, is either a phototransistor or a photodiode of some sort. I guess I will have to test it as such first, then if that doesn't work, try it as an LED. If the smoke comes out, oh well - a 5 cent part down the tubes!
To make matters worse, though, an LED can be used (in reversed-bias mode) as a crude photodetector; its not a very good one, but it can work.
Finally - about that flat-topped LED - this is usually done to make for a much wider dispersion of the light the LED produces, generally for a panel light. Some LEDs have narrow ranges at which they are brightly visible; by flattening the LED, the range is increased (at the expense of brightness). Also, on some panels they are used for aesthetic or design reasons (and depending on whether the panel will be used at an angle, etc - instead of being looked at straight on).
Hope the above helps!