Its not quite that, the thing you're describing is called helicity. Helicity and chirality are closely related, they're the same if your particle is massless fo

Its not quite that, the thing you're describing is called helicity. Helicity and chirality are closely related, they're the same if your particle is massless for example, but for massive particles they aren't the same. Imagine I have a particle which is spinning in the same direction as its linear momentum (so positive helicity) but then I speed myself up really fast so now I'm going faster than it. Its linear momentum (to me) appears to have switched sign but its spin hasn't so the helicity has flipped. Chirality is a more complicated thing which avoids this "problem" with helicity. Chirality doesn't change when the observer changed velocity.