Let $L$ be an Oriented link. The linking number $lk(L)$ is defined as follows: First choose a diagram $D$ of $L$, then

$lk(L) = \frac{1}{2} \sum\limits_c \text{sign}{\:c}$

where sign refers to the sign of a crossing of an Oriented link (see here), where $c$ ranges over all crossings of $D$ where different components meet.

See here and here

The linking number is a well-defined invariant of oriented link, that is the linking number is the same for two oriented links if they are equivalent. Therefore, if the linking number is different, they are not equivalent (standard case for Invariants)

Linking number of a Ribbon

As in here one can define the Linking number of a Ribbon by considering a the nearby, but disjoint, curve given by $X+\epsilon U$, as for sufficiently small $\epsilon$ the linking number is defined and independent of $\epsilon$. This linking number does not change if $(X,U)$ is deformed smoothly through simple closed strips ("through" here refers to the fact that each step in the deformation must be a simple closed strip, similarly to how it's done for the definition of Knot equivalence).