From what I remember the missile itself was externally the same as the original. Internally it had an INS, autopilot allowing optimal trajectory, and an IR prox fuse (upgrades that were included in the SD mk1 via a few upgrades), thus enabling terminal phase guidance. The booster was larger (longer) with TVC offering off the rail manoeuvres but also burning for a second or so longer. Testing was done with Shelldyne (Boron enhanced fuel) to increase range but I don’t recall that being within the SD mk2 baseline.
The Mk2 as contracted, was not vertical launch;- the enhanced “off the rail”manoeuvrability was to cover otherwise vulnerable arcs around the ship. That said a lot off thought and study had gone into vertical launch which resulted in a preferred method. I’ve previously put comments on this site that I was told by one of the guys who participated in the SD mk2 vertical launch concept, principally that the safety case demanded the launch cells had to be at the ships stern. However, someone with no declared detailed knowledge of the SD mk2 development, told me I was wrong, offering little more than other very different systems, decades later, possibly different safety objectives didn’t require such a consideration.