Consider it this way; a circuit diagram is any kind of diagram that illustrates how a circuit operates where the major objective is that the proper wiring of elements and their relationship to each other instead of physical location relative to one another or planning prototypes. However, in some uses classifying diagrams can be hard so accept this as general advice. I've discovered this is particularly true when dealing with much more complex circuits and electronics. I'm likely to work with a simpler but typical industrial circuit since these circuit setups are the exact same, but yet where you can observe how each sort of diagram shows the function of the circuit in their own ways.
A design diagram refers to a specific sort of circuit diagram that uses standard electrical/electronic symbols instead of pictures to show the way the circuit (or a portion of it) functions. Below is a normal 3-wire motor control circuit using a standard short stop halt - start pushbutton channel employing a schematic diagram. (Momentary this means the button/switch you trigger will go back to its default location once you physically let go of it, typically by a spring that compels the button/switch to do this.)
Here is a version of a diagram. The primary intention of this diagram will be to show the logic (referring to electrical control) of a circuit board. This diagram is the one that I mostly encounter in my own line of work, and it's extremely successful for troubleshooting problems or learning the way the circuit functions. Some frequencies are so huge that most 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's the exact specific circuit since the first two weeks, however, considering it in ladder shape.
Less clutter? I've got enough info in each one of these diagrams to know precisely what this circuit will do and where to look for problems. Hope this helps. ( Note: do not confuse lecture or circuit diagrams together with wiring diagrams; wiring diagrams will often demonstrate images of elements such as the pictorial, and also how the entire or part of a circuit is wired. The difference is that wiring diagrams typically place an emphasis on actual physical place of necessary elements relative to each other that essentially tell a layman exactly what to do about the wiring)
Here is another schematic diagram demonstrating exactly the identical circuit, connections and components and it looks different but they both fall into precisely the same category.
Pictorial design diagrams, or pictorial circuit diagrams are basically the exact same thing with exactly the identical function, however they use images of elements inside the circuit instead of symbols. Again, here's the exact identical specific circuit (virtually except a control transformer was inserted and they are utilizing conductors L1 and L3 rather than L1 and L2.