How does the definition of strong nuclear force differ between astronomy and physics?

There is no difference.

Astronomy is, essentially, applied physics (with the relatively recent developments of astro-chemistry and astro-biology, this isn't as clear cut as it used to be, but overall I think it still applies), so terms from physics migrate over to astronomy with no change. The definition of the strong nuclear force (which is the force that keeps protons together in the nucleus of atoms) is included in this.