When a company issues a number of common shares, some of which areheld by institutional...

The shares held by institutional investors, along with other shares available for trading by the public, are referred to as thepublic float shares. These are the issued shares of a company that are actively traded in the market, excluding restricted shares held by insiders or strategic investors.

Other options:

Issued shares: Includes all shares a company has issued, including restricted shares.

Outstanding shares: Includes all shares held by all shareholders, including restricted shares and shares not available for trading.

Market capitalization shares: Not a term used to describe shares; market capitalization is a measure of a company's total value based on its stock price and outstanding shares.

References:

Volume 1, Chapter 8:Equity Securities, section on "Public Float and Market Capitalization" explains the concept of public float shares​.