The order you've given the 3 systems in, gets more specific/modular as you go through it.
electrical systems tend to use older components of what we'd now include within the general term electronics (so stuff like capacitors, resistors, and relays, sometimes thermionic valves, but very very rarely discrete transistors) They're often analogue systems (sometimes it can be better than digital!)
electronic tends to mean transistors, and/or basic Integrated circuits (so things like the 7400 series chips, 555 timers etc) when wired up correctly the do the "thinking". There is no software
computer based systems have a single (or very few) complicated chips handle the "thinking", and a few relays/transistors which concentrate on interfacing with the "real" world. Used to be the Z80 chip, but now much more likely to something like a PIC micro-controller. They NEED software, or firmware (software that's embedded in) to do their job.
The more physical components needed to build a system, the higher the chance of failure. As there's more individual components to be soldered in place the cost per unit tends to higher for all but the simplest systems.
electrical systems where the first step in replacing purely mechanical systems.
electronics started modularising common sub-systems used in electronics, and placing those sub-systems up into convenient "off the shelf" integrated circuits.
Computer based systems then started splitting the system into 3 areas, inputs, outputs and control, and continued the process of packaging components with similar jobs into fewer chips. As the control section are usually controlled by an easily replaceable chip, (or even by eePROM contained within it) it's fairly easy to make major changes to the precise functioning of the control, simply by changing a single chip, or connecting a programmer to the control chip. The limiting factors then becomes the allowable complexity of the system to be controlled, and the devices which are plugged into the control chip. More of the design/testing can be done on computers, speeding up design to production.
I'll have a shot at the final part. (I've been awake way too long, so hope it's coherent!)
A telephone exchange has examples in each of these paradigms,
The electrical version used often used relays, to switch calls.These tended to wear out, and it was very difficult to add features to the system, as the number of relays were limited by reliability, heat and the power they consumed
electronic systems initially replaced the relays with transistor switches, but latter several transistors were grouped onto single chips. Later still additional transistors/chips were added which easiest the management of the exchange and enabled additional features to be added (but still with difficulty)
computerised exchanges have far more advanced control systems, and ALL functions of the exchange can be controlled/tweaked remotely. The exchanges can decide on the best route for calls to take They also make better use of the physical lines between exchanges, because they can compress the data that's sent.When the complexity of the system, is taken into account they are much easier to manage. Much easier to add features. (OK so if testing isn't thorougher any bugs which do occur can be much more difficult to route out)