Generally speaking, limerick is a kind of rhyming folk word-of-mouth poem, which is easy to understand and has not risen to a high literary level.
Poetry, this definition is also quite broad, such as the Book of Songs, which just sounds comfortable and catchy to read.
Ci, generally speaking, is Song Ci, which has a certain name, and was sung at a concert.
Generally speaking, they all belong to poems and songs. In modern times, the format is not particularly dead, so prose poems and modernist poems appear in large numbers. But if you are interested, I suggest reading more Tang poetry and Song poetry. Maybe you can find your own answer.