There is a difference, but it does not make one rx & the other OTC.
Both Anaprox & Naprosyn DS (& its generic equivalents) are both naproxen sodium. They have the same base molecule as the generic naproxen, but with an added sodium in its bonding.
The only advantage the sodium molecule adds is its more rapid (not statistically significant) absorption & deeper penetration (which is significant) into some tissues - the uterus is the prime example of this.
The rx designation is tied to the mg amount only, not the ion it is bonded to. However, by marketing the sodium molecule to naproxen, it definitely makes it marketable & effective to the market of of premenstrual cramping. Beyond the 220mg amount of naproxen sodium or 200mg amount of ibuprofen, you get to the rx products.
I hope that clears it up a bit.