The most significant and obvious change is that pirates are a separate faction. In SR2, pirates are regular ships, which means that if you blow up a Maloq pirate, you piss off the Maloqs. In SR HD, all pirates, regardless of the race of the ship/pilot, are considered part of a Pirate faction. Blowing one up pisses off the pirates, but not the race of the pirate pilot.
Being a pirate yourself is more viable, since you can prey on civilians to your heart’s content and the pirate-controlled star systems will remain friendly. In SR2 piracy pissed off enough governments that getting repairs would quickly become rough. Despite this, I’d still say going full pirate is still impractical. Combat just isn’t economically rewarding, you take enough damage that the loot barely pays for repairs. Trading and missions are still the ways to go.
The pirate faction makes the game somewhat harder, because they blow up vital Research and Ranger stations when they take control from civilians. Fights between the pirates and the military weaken system defense against the Dominators.
There’s a new Pirate career. If you elect to go pirate, you advance in the Pirate ranks instead of the military ones. In the Pirate career, you score points pretty much like the military one, except that you get points for blowing up civilians in addition to Dominators. However, you don’t get promoted automatically when you pass a score threshold, you have to complete a mission, which makes the pirate track more interesting. The rewards are a little better too. A couple of those involve piracy, but you can otherwise walk the straight and narrow by blowing up Dominators for points to advance.
Beyond the piracy stuff, there’s a new set of adjectives that apply to equipment, including hulls. These have drawbacks in addition to bonuses. Some of these are good, some are so terrible you’ll never want to take an item with that modifier. For example, anything that reduces ship speed is very bad, no matter what bonuses it provides. As with SR2, most equipment is normal stuff without an adjective, so you don’t have to put up with any drawbacks you don’t want.
The search box for luxuries is fixed. In SR2 if you searched for luxuries specifically by price, the game searched for minerals instead. Which meant for trading you really had to just search for all nearby planets and eyeball the luxury costs manually.
Otherwise, it’s pretty much the same.