What will be the difference in the behaviour between electric charges and between magnetic charges? It’s often asked in PSE about the existence of particles with magnetic monopoles. What’s the difference in interaction between magnetic monopoles and electric monopoles in such a theoretical case?
Edit: Could the question implies that on the level of subatomic particles the search for or a claim of the existence of magnetic monopoles simply doesn’t make sense? Because, or they will not be distinguishable from electric charges, or would not interact with our surroundings.
 A: Magnetic monopoles respond to magnetic fields in the same way as electric monopoles (more commonly called charges) respond to magnetic fields.
According to the Lorentz force law, in an external electric field $\vec{E}$ an electric charge $q$ will feel a force $q \vec{E}$. A magnetic monopole of charge $g$ in a magnetic field $\vec{B}$ will feel a force $g \vec{B}$. If we have both magnetic and electric fields present, and the charges have velocity $v$, the force law is
$$\vec{F}_\mathrm{q} = q(\vec{E} + \vec{v} \times \vec{B}),$$
$$\vec{F}_\mathrm{g} = g(\vec{B} - \vec{v} \times \vec{E}).$$
If monopoles exist, the laws of nature are symmetric under $q \leftrightarrow g$, $\vec{E} \to \vec{B}$, $\vec{B} \to -\vec{E}$. This is known as electromagnetic duality, and its 'beauty' is the reason why people first started wondering if monopoles existed (we have better reasons now!). But this doesn't mean that monopoles and electric charges will behave identically. Because in this universe there are an abundance of electric charges but no observed magnetic ones, it would be very easy to spot a monopole! For example, we can see from the equations above that in an electric field a stationary monopole would feel no force, while an electric charge would be accelerated.
