Think of it this way; a circuit diagram is any kind of diagram that demonstrates the way the circuit operates where the major purpose is that the appropriate wiring of components and their relationship to each other rather than physical location relative to each other or intending prototypes. Nonetheless, in some uses classifying diagrams can be difficult so choose this as overall advice. I've discovered this is particularly true when working with more complex circuits and electronic equipment. I'm likely to work with a more straightforward but average industrial circuit since these circuit set ups are the exact same, but yet where you're able to see how each sort of diagram indicates the use of the circuit in their own manners.
A schematic diagram refers to a specific type of circuit diagram which uses standard electrical/electronic symbols rather than pictures to demonstrate the way the circuit (or a portion of it) works. Below is a standard 3-wire motor controller circuit employing a standard momentary halt - start pushbutton station employing a schematic diagram. (Momentary here means the button/switch you activate will go back to its default location once you physically let go of it, usually by a spring which forces the button/switch to do this.)
Much less clutter? I've got enough information in all these diagrams to know precisely what this circuit will do and also where to start looking for problems. Hope that this helps. ( Note: don't confuse lecture or circuit diagrams together with wiring diagrams; wiring diagrams will often show 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 real physical place of necessary components relative to each individual that basically tell a layman exactly what to do concerning the wiring)
Pictorial design diagrams, or pictorial circuit diagrams are basically the exact same thing with exactly the same purpose, however they use pictures of elements inside the circuit rather than symbols. Again, here's the identical precise circuit (virtually except a controller was added and they are utilizing conductors L1 and L3 rather than L1 and L2.
Here is another schematic diagram demonstrating precisely the identical circuit, components and connections and it seems different but they fall into the identical category.
Here's a specialized version of a diagram known as a ladder design. The primary goal of this diagram will be to show the logic (referring to electrical control) of a circuit. This really is the one that I mainly come across in my own line of work, and it is very successful for troubleshooting issues or learning the way the circuit works. Some frequencies are so huge that most types of schematic diagrams need to be recorded in increments in book form (usually with coded numbers so that information can be simpler found). Again, here is the same exact circuit as the first 2, however, looking at it in ladder shape.