Equity Capital: A company sells $1m worth of stock. It records an increase of $1m cash (an asset) and $1m equity. Assets - Liabilites = Equity.
Then there is the case of debt capital.
Debt Capital: A company sells $1m bonds. Assets increase $1m (cash from loan), Liabilities increase $1m, net effect on equity $0.
Equity = Capital + Retained earnings
Capital is part of equity.
Depends on the context. Capital can refer to equity or debt needed to fund a business. Capital goods are assets that are bought to increase future production.
Context is everything!