Pulstar was developed by Aicom. Blazing Star was developed by Yumekobo. They technically aren't sequels, although, they share numerous playmechanics in common:
Hold down the fire button to use a charge shot.
By tapping the shot button very fast, the standard shot becomes more powerful.
The Dino 246 is playable in both games.
Pulstar has a very R-Type-ish weapon system (no real surprise considering that some ex-Irem employees were the core of Aicom). Pulstar is more memory-driven (again, see Irem) and has a very straighforward score system.
Blazing Star has a more general power-up system (each ship can power-up four times, done by grabbing a universal capsule). The game is more kinetic than Pulstar, and relies more on bullet interaction. Blazing Star also features numerous high-score tactics and bonuses (in the form of various chaining systems and multipliers).
Both games used heavy amounts of pre-rendering to generate the sprites. No doubt that the inclusion of the Dino 246 and the Dino 135 from Pulstar were results of prior Aicom staff helping out Yumekobo with the graphics engine.