What is the difference between merge down, merge visible, and flatten image?

Hi there,

  Merge Down combines the layer below the currently selected layer and the selected layer together into one singular layer. The layer name will change to the name of the layer below the selected layer. In the screenshot below, I chose to Merge Down from the layer "Circle Top". As you can see, afterward I have a new layer named "Circle Below" that has both layers combined.

  Merge Visible will merge all visible layers into one singular layer. Merge Visible will ignore any layer that has it's visibility toggled to "Off".  In the example below, I have 4 layers, with the layer "Circle Below"'s visibilty set to "Off". After I choose Merge Visible, all of the layers are combined excluding "Circle Below".

  Flatten Image will combine all of the layers into one "flattened" image or layer. You will be prompted to choose whether or not to discard hidden layers before doing so. If you choose "Ok" to discard hidden layers, Photoshop will ignore any layer with it's visibility toggled to "Off". If you choose "Cancel", Photoshop will cancel the flattening process. If you want the hidden layer included in the flattened image, you will have to toggle it's visibility to "On". The following screenshot is what a flattened image's layer pallete looks like:

  I hope this helps! If you need further clarification on this let me know! : )