Let's review first these two computation processes to see if in their core fundamental nature are actually different:
1) Quantum Computing
One of the properties of quantum mechanics that is exploited in QC is that the qubit is represented as the superposition of the spin of an atom or electron when subjected to a switching polarity homogeneous z-axis magnetic field $B$ for example for the case of an electron:
Discrete logic values of qubit
The electron can be arbitrary land at any of the above states when the external magnetic field $B$ is switched on at a specific magnetic moment (N pole up or down). In the above illustration the z-axis $B$ field assuming it has its magnetic moment vector pointing up (N pole up) for the electron on the left-hand side, has its spin precession cone facing up, is called a spin up electron and its magnetic moment vector facing down antiparallel to its spin vector and $B$ field magnetic moment vector (i.e. electron has negative electric charge therefore its magnetic moment is always antiparallel to its spin angular momentum vector). This state is the highest energy state of the electron and represents a discrete value of a logic $1$ qubit. The right hand-side electron, spin down has its magnetic moment aligned parallel to the $B$ field and is in the lowest energy state and is called a discrete value logic $0$ qubit.
Furthermore, we can take advantage of the magnetic precession of the electrons, magnetic vector of electron rotating around 360° the z-axis $B$ field (see blue cone) and apply an analog linear amplitude operator, continuous value, to correspond the the electron's magnetic moment position around the rim of its precession cone assuming we know the precession frequency which depends on the strength of the external magnetic $B$ field (see Bloch Sphere below).
Bloch Sphere
So, wee see now that we can encode in a single qubit more information than a normal binary bit since for fully describing its quantum state we need its discrete logic (binary) value 0 or 1 but also its logic 0 analog amplitude operator and also logic 1 analog amplitude operator:
$$
|\psi\rangle=\alpha|0\rangle+\beta|1\rangle \quad \alpha, \beta \in \mathbb{C} \quad|\alpha|^{2}+|\beta|^{2}=1
$$
The situation rises exponentially when we have $N$ number of quantum entangled qubits where we can encode information translated in binary logic of $2^{\mathrm{N}}$ normal bits.
All the above mentioned is the so called setup phase where we prepare our entangled qubits at the desired quantum state using the magnetic $B$ field accordingly to the computation we want to perform and then zero the $B$ field for an amount of time. During the zero $B$ is when the "magic" happens. The entangled correlated qubits start interfering in superposition and when we switch back the external $B$ field we quickly sample the quantum states of the qubits and voila the answer to the computation asked. Since there is only one basic arithmetic function namely algebraic addition (i.e. multiplication is sequential addition and division sequential subtraction) the trick to quantum programming is to set correctly all qubits at the desired quantum state during the setup phase, input of the computation. Notice here, from the computed final answer we extract only the discrete quantum states logic $1$ and $0$ thus binary information as we would have in a normal binary computer.
2) Analog Computing
Although over simplified, fundamentally in an analog computer if we want say to add 0.866 with 0.344 we would send these two analog linear current values say 0.866μΑ and 0.344μΑ in a known resistance value ohmic resistor and read the corresponding voltage drop on the resistor. Usually in practice this is done with an analog opamp circuit called adder:
V1,V2 and V3 analog numbers are added at the output of the circuit $V_{O}$
image source: https://electronics.stackexchange.com/questions/392292/adding-large-numbers-in-context-of-analog-computing
$Question:$
We observe above in case 2 of analog computing, that the computation and input data as well as output are pure analog linear continuous values taking advantage of the natural algebraic analog addition of electric currents phenomenon similar fundamentally to case 1 quantum computing, where the total superposition quantum state (i.e. discrete quantum state with analog operator amplitude values) of the entangled qubits during the zero magnetic field phase where the actual computation takes place and the interfering spins are in superposition thus can take any arbitrary continuous value (i.e. analog).
So, if the wave function amplitude is a continuous quantity at the core of the quantum computation (i.e. zero magnetic $B$ field phase) is in that sense, quantum computing actually analog?
Best Answer
Quantum computers are like classical analog computers in that they have a continuous state space, and are like classical digital computers in that they have a discrete output space.
Anything beyond that is just opinion about what the words "analog" and "digital" ought to mean. In my experience, quantum computers are rarely called either analog or digital. They're just called quantum.