As other comments note, this is not the definition of a linear system. However, it is the definition of a time-invariant system, which is probably why it's coming to mind here.

Systems that are both linear and time-invariant, sometimes abbreviated to LTI systems, are the most common sort of thing (i.e., model) that one actually analyzes. When time-dependence is present, it is always modelled explicitly and usually modelled as a complication of a time-invariant system.

>means that you get the same output from a circuit

Not sure where you were taught that, but it does not strike me as the generally accepted meaning of the term "linear".

Where I hail from, linear means:

    f(a*x + b*y) = a*f(x) + b*f(y)

aka the superposition principle.

A linear circuit is one which obeys the superposition principle. Its easer to analyze under frequency domain for example.

https://en.wikipedia.org/wiki/Linear_circuit

Capacitors are linear but stateful, so would be memristors. I am not sure you characterization is correct.

That's just not true. Its a very specific relation between the output and the input of a system.