There are significant gameplay differences. TL;DR void war has way more crew, an equipment system, a larger focus on crew combat, more ship armament and system types, and way more difficulty options.
While FTL has 8 crew types, Void War has 99 (at the time of writing), which each belong to 7 or 8 different factions with unique characteristics (all Death Cultists are poison immune, almost all Blood Cultists interact with thralls in some way, and so on). Most crew also have different amounts of equipment slots where they can equip different armor, weapons, psychic abilities, and so on.
The game is more focused on crew combat: units with the ability to teleport around are common, boarders are plentiful, and since each run starts with you choosing a powerful Commander unit, you can start boarding right away.
Or you can summon Ghouls on the enemy ship to board for you. Or you can send your Sub-Husks straight from the factory into the assault sled to overwhelm the enemy with numbers. Or all three at once.
Aside from that, there are a ton of different systems, Missile and Siege/Artillery weapons work differently, traversing through the sector works more like STS than FTL, the Lance weapon type is around, there's 6 sectors instead of 8, there's 3 bosses instead of 1, and there are 13 difficulty options instead of 3.