Русско-англо-русский юридический словарь

Sometimes, shares of stock offered by a company are not regular, market-driven common shares. Instead, they may be preferred shares, which are considered fixed income securities and are issued with a par value. When that par value is paid back to the purchaser of the preferred share, this is considered a redemption. (Investopedia)

When a company issues shares of common stock for the public to buy and later decides to buy some of those shares back, that's considered a repurchase rather than a redemption. The major difference between the two is that the shares bought back in a redemption are considered a fixed-income security that is expected to be bought back by the issuer. A repurchase of shares, however, reduces the number of outstanding shares that a company has, and can increase the company's holdings so that it remains or regains majority shareholder status. (Investopedia)