Is an inner bailey and an inner ward the same thing?

Answer 1

No, they are different. The Anglo-Norman word bail, ballie or baillie signifies an area attached to a motte-and-bailey castle with a ditch, bank and wooden palisade defence around it. There are often (not always) two.

The term ward is from Anglo-Norman garde, which when applied to later stone castles is an enclosed area with its own unit of guards - there can be many wards within a castle complex, each capable of being isolated from the others. The same word can also refer to zones within a town or city, each again the responsibility of a unit of Watchmen or guards.