These are some definitions I'll be using in the near future. For my purposes here I will use the following rough meanings to talk about things which are strong visual elements in a photograph (or painting, or really any visual medium). There are probably better words for these things out there, but I don't know what they are.
Symbol - a visual element which stands in, for most viewers, for a larger idea. A 1950s era diner, a destitute mother, a cross, a swastika.
Mandate - a visual element which may or may not be symbolic, but which most viewers insist upon whether they know it or not. Attractive clouds in the sky over a landscape, for instance. Clapboard siding should be either unpainted, or white. Old farm equipment must be shown with grass grown up around it.
Cliche - a visual element that appears widely in photographs, but which carries no special symbolic weight for most, and which the view does not require in the same way they demand a "mandate". Moving water that is blurred by a long exposure is a cliche. The homeless man sitting on a curb is also a cliche, but could also be considered a symbol.
The idea of a symbol overlaps with the other two categories. A mandated visual element might also carry symbolic weight, and so on. The point is that a symbol carries a freight of largely pre-defined meaning, for most viewers.
Cliches and mandates do not really overlap, because they are defined in opposition to one another. A cliche, by definition, is not a mandate. If you like, you might consider a symbol something that carries meaning, and cliche/mandate to be a spectrum describing frequently occurring visual ideas. Both are things that are commonly done, mandates because viewers demand or like it, cliches typically because the photographer likes it.