In all cases, the use of the term "capital" is to denote that the security is relatively junior in the issuing corporation's order of priorities in claims for its assets.
Alternately, a capital note is a bond with a very long maturity horizon, reaching several decades (sometimes as much as 50 or 100 years).
However, since their maturity is so far in the future, they are treated as equity for practical purposes; the company keeps the money raised through them inside its balance sheet for a very long time.
Banks and other financial institutions issue these bonds to satisfy regulatory demands regarding capital requirements, specifically under the Basel Accords.
Additionally, bank capital notes are usually not collateralized and are contractually subordinated, forming a junior class of debt.