Here is a specialized variant of a design diagram called a ladder structure. The principle intention of this diagram will be to demonstrate the logic (referring to electrical control) of a circuit. This really is the one that I mostly encounter in my own line of work, and it's very successful for troubleshooting issues or learning how a circuit functions. Some circuits are so enormous that many types of schematic diagrams need to be read in increments in book form (typically with coded numbers so info can be easier found). Again, here is the same specific circuit because the first two weeks, however, looking at it in ladder form.
Right, Less clutter? I've got enough info in all these diagrams to know just what this circuit will do and also where to start looking for problems. Hope this helps. ( Note: do not confuse circuit or schematic diagrams with wiring diagrams; wiring diagrams will typically demonstrate images of elements such as the pictorial, and also the way the whole or part of a circuit has been wired. The difference is that wiring diagrams typically place an emphasis on actual physical location of necessary components relative to each other that basically tell a layman Just What to do concerning the wiring. )
Consider it this way; a circuit diagram is any sort of diagram which illustrates how a circuit functions where the primary goal is that the proper wiring of elements and their relationship to each other rather than physical place relative to one another or planning prototypes. However, in some applications classifying diagrams can be difficult so do this as overall advice. I have found this is particularly true when dealing with much more complicated circuits and electronic equipment. I'm going to work with a simpler but typical industrial circuit because these circuit setups are the exact same, but where you're able to see how each type of diagram shows the function of the circuit in their own ways.
Pictorial schematic diagrams, or graphic circuit diagrams are essentially the identical thing with exactly the same purpose, however they use images of elements inside the circuit rather than symbols. Again, here is the exact identical precise circuit (virtually except a controller was added and they are using conductors L1 and L3 instead of L1 and L2.
Here's another schematic diagram demonstrating the identical circuit, connections and components and it seems different but they both fall into precisely the exact identical category.
A design diagram refers to a specific type of circuit structure that utilizes standard electrical/electronic symbols instead of images to demonstrate how a circuit (or part of it) functions. Below is a standard 3-wire motor controller circuit using a typical momentary stop - start pushbutton station utilizing a schematic diagram. (Momentary here means the button/switch you trigger will go back to its default place once you let go of this, typically by a spring which forces the button/switch to do this.)