Remington-Peters bullet question

I have a question concerning the older (1940-1960) era bullets offered by Remington and Peters. Since they were both the same ownership, were the bullets Peters used the same as and produced by Remington? The bullets I am interested in are the Remington Mushroom Core-Lokt and the Peters inner belted hollow point. Are these the same bullet? They do have different cannelures but that is the only difference I see.

The Peters Belted was a popular hunting bullet prior to WW2 but had some faults. Remington introduced their Core-Lokt design, eliminating the outer belt, instead swaging the jacket with a heavy section on the inside. Peters then discontinued the Belted Bullet, adopting the Remington type. They called theirs Inner-Belted. So, yes, they are essentially the same bullet.