What is the difference between "al-raḍāʿa" (with an open raʾ) and "al-riḍāʿa" (with a kasra on the raʾ)?

There is no difference between "رضاعة" (radhā‘ah) with an open ra' and "رضاعة" (riḍā‘ah) with a broken ra'. Both mean "رضاع" (raḍā‘), which is a second masdar (verbal noun) for the verb "رضَعَ" (raḍa‘a - to suckle).