All internal quantum numbers are inverted (baryon number, lepton number etc).
When thinking about antimatter, it is important to not think of it as being the 'opposite of matter', but to think of it's defining property as being that it will annihilate with matter to produce energy.
Once we think about it this way it is clear that any quantum numbers, which are conserved in particle interactions, must be inverted in an antiparticle, in order to conserve the number in the overall interaction of annihilation.
To answer the second part of your question, I believe that the identities of particles are typically found by observing their paths in cloud chambers, or in more modern terms, the detectors of particle accelerators.
This process involves looking at the direction that the particle curves in a magnetic field, but also looking at the way the particle decays.
In nature fundamentally, there is a difference seen between matter and antimatter. Beta decay disobeys P-symmetry, meaning that the world would not be symmetrical under a mirror image of itself. This was found in beta decay of cobalt 60, where the emitted electrons were preferentially emitted in the opposite direction as the gamma rays emitted; this meant that most of the electrons were emitted in the direction opposite to the nuclear spin. This showed a violation of P-Symmetry as the universe would not look the same, in this experiment, under a mirror image of itself.
What was found however is that this phenomenon, a weak interaction, was symmetrical under CP-Symmetry, meaning that a universe would appear the same as it's mirror image if all internal quantum numbers were also inverted ( the matter was swapped with antimatter). This shows that on a fundamental level, there is a difference between matter and antimatter, as a swap of internal quantum numbers (antimatter), will also require a reflection of coordinates (right to left hand) in order to preserve symmetry.
Put briefly, the weak interaction is not symmetrical under an inversion of charge (and by charge I mean an inversion of all internal quantum numbers). By this, it follows that our universe would not look the same as one in which all matter was replaced with antimatter, and so, yes, there is a fundamental difference between matter and antimatter.
Up until now, we have thought that all forces are symmetrical under CP-Symmetry, however, there has been some debate about CP violation in the decay of the neutral kaon, however, I feel like I have already gone beyond the scope of the question.
Hope this helps.