Single black & rich black are both different composites of black. An can be used for varying effects.
Single black when in photoshop is a hundred percent K. Rich black is a mix of the composite colours. Cyan – 75%, Magenta – 68% , Yellow – 67%, Black – 90%. This could cause problems if you where then inputting images from photoshop created with the single black, as it differs from other adobe suite programmes.
Problem is you wouldn’t be able to tell until the item went to print came back an you had to altering shades of black. Making the image therefore stand out more , rather than blending. Would only occur when transferring items from photoshop as they use the composite colour black.
With both InDesign and Illustrator there is a preference setting called “Appearance of Black” which can be set to display blacks “as black” or “accurately.” For print work always set these to display and print blacks accurately so you don’t make an error.