We mean compatible as defined by the C language standard. It is much more restrictive than having the same layout. In particular, you may not pass a pointer to a type where a pointer to an incompatible type is expected, even if the types have the same layout, which prevents the sort of sharing between two libraries that is being discussed.

Moreover, there is no guarantee that two distinct structure types with the same list of members have the same size or alignment (although in practice they do). The members must nevertheless be laid out in the same way (same offsets, and in the case of bit-fields, same layout inside storage units) due to an obscure constraint on common initial sequences. So the layouts of the structures may differ in the alignment requirement and the amount of trailing padding.