Yes, there is a difference. If a person's private parts are exposed while he is praying, and he immediately covers himself, his prayer is not invalidated. Rather, it is invalidated if a specified time passes, which is if he performs a pillar of the prayer in reality while exposed, according to Muhammad (may Allah have mercy on him). According to Abu Yusuf (may Allah have mercy on him), it is if a time passes during which it is possible to perform a pillar of the prayer – that is, the duration of three tasbihs. In contrast, if the exposure occurs at the beginning of the prayer, it prevents the prayer from being valid if it is the size of a quarter of the limb or more; because covering the private parts is a condition for the validity of starting the prayer, and without it, the commencement is not valid. See: Maraqi al-Falah, pp. 210-211, Al-Wiqayah and its explanation by Sadr al-Shari'ah 1: 143, Radd al-Muhtar 1: 408, Badā'i al-Sanā'i 1: 117, and Al-Hadiyyah al-‘Alaiyyah, p. 72.