Ann: Trading Halt, page-64

A Google on 'equity raising vs capital raising' returns a lot of results that include 'equity capital raising' suggesting to me capital raising and equity raising in the context of a public company are the same thing.

Equity - the value of the shares issued by a company.
"he owns 62% of the group's equity"

Capital - wealth in the form of money or other assets owned by a person or organization or available for a purpose such as starting a company or investing.
"rates of return on invested capital were high"

IMO all equity is capital, but not all capital is equity.