This might help. Dictionary defines ʻai as "Food or food plant, especially vegetable food as distinguished from iʻa, meat or fleshy food; often ʻai refers specifically to poi..."
There is a similar usage in Japanese where 'rice'/'gohan' can also mean 'meal' e.g. asagohan (morning rice)= breakfast
Weren't we using a different word for poi?
Yes, sometimes it's "ka poi" and sometimes "ka 'ai," but I wish there was a note or something somewhere to explain the difference and when to use one of the other.