what is the difference between city limits and corporate city limits?

Answer 1

In reality -- nothing.

Almost all cities nowadays are incorporated, so the city limits are the corporate city limits -- the limits of where the city (which is a corporation) has authority.

In outlying rural areas -- or some less developed countries -- cities may exist which are not incorporated -- so the city limits may exist as the extent of the city infrastructure, but there are no corporate city limits because the city is not incorporated.