NS Capture vs NS Creation Diagrams
NS Creation explains the observations of supernovas resulting in fast pulsars by asserting a giant stars collapse under their own weight and expel their outer layers. The result is a compact star supported by neutron degeneracy pressure which conserves it’s angular momentum and thus becomes a fast pulsar.
In order to explain the observed NSs spinning up in the presence of GSs, we need to explain the origin of the GS+NS(0) binary.
NS-Creation explains the NS(0) with 2 GSs. One goes through the NS Creation process above.
In some cases, we instead begin with an NS and a GS. The NS is captured by tidal forces and a binary is formed. Then the NS spins up into a FP until the GS goes supernova leaving a FP(-) which will become in an NS(0) after spinning down.