Are the stars making up these constellations, Hercules and Sagittarius, travelling at similar speeds?

The Sun is 8 kiloparsecs from the galactic center.

All those stars are relatively nearby, within 500 parsecs, and are mostly traveling in the same orbit as the Sun --- 235 kilometers per second around the galactic center. But on top of that motion, there's a random component, different for each star, that's about 25 kilometers per second. As a result, the constellations will become unrecognizable after a few thousand years.

So, the further in toward the center of the galaxy, the faster stars move in their orbits. (There's some play here, but we'll gloss over that for now...)

So, if Earth is about as far out as the stars making up Hercules, we'll be orbiting at about the same speed as those stars. Since we're looking toward the hub of the Milkyway when we look at Sagittarius, then that means the stars of Sagittarius are *closer* to the center than we are - and they'll be orbiting a little faster.

Sagittarius is being consumed by the Milky Way as we speak.