Consider it this way; a circuit diagram is any type of diagram that illustrates the way the circuit operates where the primary objective is that the appropriate wiring of components and their relationship to each other instead of physical place relative to each other or intending prototypes. However, in some uses classifying diagrams can be hard so take this as general advice. I've discovered this is particularly true when working with more complex circuits and electronic equipment. I'm going to work with a more straightforward but average industrial circuit since these circuit set ups are the exact same, but where it is possible to observe how each kind of diagram indicates the operation of the circuit in their own ways.
Here's a variant of a schematic diagram known as a ladder design. The major aim of this diagram will be to show the logic (referring to electrical control) of a circuit. This diagram is the one I mostly come across in my line of work, and it is very successful for troubleshooting issues or learning how a circuit works. Some circuits are so huge that many types of schematic diagrams have to be recorded in increments in book form (typically with coded numbers so that information can be easier found). Again, here is the exact identical exact circuit since the first two, but looking at it in ladder type.
Here is another schematic diagram demonstrating the same circuit, connections and components and it looks different but they both fall into exactly the exact same category.
A design diagram refers to a particular type of circuit design which uses standard electrical/electronic symbols rather than pictures to demonstrate how a circuit (or portion of it) works. Below is a typical 3-wire motor controller circuit employing a normal short stop halt - start pushbutton channel using a schematic diagram. (Momentary here means the button/switch you trigger will go back to its default location once you let go of it, usually by a spring that forces the button/switch to get this done.)
Right, less clutter? I have enough information in all these diagrams to know precisely what this circuit does and where to start looking for issues. Hope this helps. ( Note: don't confuse circuit or schematic diagrams with wiring diagrams; wiring diagrams will typically demonstrate pictures of elements such as the pictorial, and the way the entire or part of a circuit is wired. The difference is that wiring diagrams typically put an emphasis on real physical location of necessary components relative to each other that essentially tell a layman Just What to do concerning the wiring. )
Pictorial design diagrams, or pictorial circuit diagrams are basically the same thing with the same function, however they use images of elements inside the circuit instead of symbols. Again, here's the exact same precise circuit (almost except a controller was added and they're utilizing conductors L1 and L3 rather than L1 and L2.