Why do we need small signal analysis in differential stage?
For example, if I consider the classic non inverting configuration of an op-amp with a constant generator (For esample, 5V) I don't see a sinusoidal signal between the 2 input terminals of the op-amp (the voltage between them is approximately 0)


You don't, if the amplifier is stable. If it's unstable, you'd certainly see something oscillating. If for instance you added a large capacitive load to the output, or a large capacitive stray to the inverting input, then that could send the amplifier unstable, even with a constant input.

How can you tell whether the amplifier will be stable or not? You do a small signal analysis of the amplifier, together with its load, external components and stray components.

Most of the time, we don't need to bother with this, as most op-amps are designed to be unity-gain stable. This means slow ones can usually be flung into a circuit in any configuration with impunity. However, use a fast one, or use one into a difficult load, and you have to know what you're doing, or follow advice in the application note, to get them to behave.