What are the Differences between Analog and Digital Devices?
Everything is analog / analogue !

Digital is a simplification of analog, instead of that a voltage can have any value between 0 and 5 V, for example 1.23456789 V (Analog) we only consider 2 states: 0 V and call it "0" and 5 V and call that "1".

That is regarding signals and you already knew this.

You can do something similar with circuits and devices. In essence, all circuits and devices are Analog, yes even that CPU in your PC. The voltages inside it are not "0" or "1" they're 0.002338 V or 1.23328 V.
But to make things easier we make an abstraction and say it's either zero or one.

However the core functionality of that CPU or any other digital device can be described fully when considering only the zeros and the ones. So in my opinion, if you can fully describe the functionality of a device with only ones and zeros, it must be digital !

Coming back to the 555 timer. Note that part of its functionality is to charge a capacitor, that voltage can have any value between a lower and an upper threshold. I call that analog behaviour. Inside the 555 there is a flip-flop which has two states, you could call that digital.

So the 555 is more of a mixture, mostly analog but with a bit of digital.

Most CPUs and MicroControllers are considered digital although some CPUs have voltage regulators and/or a PLL (with an Analog oscillator) inside and/or an ADC which is very Analog indeed. And yet, no-one calls CPUs and MicroControllers analog devices (but secretly they are !)