Is what the Companion meant by saying "I pledged allegiance" in this Hadith the pledge of allegiance to Islam? And what is a pledge of allegiance, and what are its types?

The aforementioned hadith was narrated by Ahmad, and its narrators are trustworthy, but it is considered defective due to اضطراب (idhtirab) (discrepancy) and معارضة (mu'aradah) (contradiction) in its narrations. However, Al-Albani authenticated it, concluding that it has three sound chains of transmission and that it is authentically established from the Prophet, peace and blessings be upon him. The narrations do not specify the type of pledge mentioned, whether it was a pledge of Islam or otherwise, and this does not entail a significant implication. For, the Companions shaking hands with the Prophet, peace and blessings be upon him, is established, while the women's pledge was by word without handshaking.