There was also some discussion in here aboot this a while back; the specification for 75Ω BNC appears to also include a different diameter center pin, which is not always adhered to. I ran into this with some of my Crestron service calls back in the day; a BNC that had the center socket damaged by insertion of the wrong type BNC plug and no longer made proper contact.
It does, and it has to. The impedance of a coaxial connector/cable is governed by:
\[ Z_0 = \frac{138\ log{\frac{D}{d}}}{\sqrt{\epsilon_r}}\]
where \$Z_0\$ is the characteristic impedance, \$D\$ is the diameter of the outer conductor, \$d\$ is the diameter of the inner conductor and \$\epsilon_r\$ is the relative
permeability permittivity of the dielectric. As the outside diameter is fixed by the connector geometry it follows that to get the desired impedance the diameter of the inner conductor, the pin,
has to change.
edit:
permeability permittivity - I'm always getting that one wrong. I blame the people who decided that electromagnetism needed two parameters that shared more letters than they differed by.