What is the difference between saying "Astaghfirullah" (I seek forgiveness from Allah) and "Allahummaghfirli" (O Allah, forgive me)? Is the first a form of remembrance (dhikr) and the second a supplication (du'a)?

The two phrases, "Astaghfirullah" (I seek forgiveness from Allah) and "Allahummaghfirli" (O Allah, forgive me), have no difference between them. Both fall under the general category of Dhikr (remembrance of Allah), and both are supplications for seeking forgiveness from Allah. The Prophet, peace and blessings be upon him, used to seek forgiveness three times after his prayer, saying "Astaghfirullah," as explained by Al-Walid to Al-Awza'i.