Shares outstanding is the total number of shares a company has issued. Market cap is that number multiplied by the current share price — the total dollar value of the equity. Shares outstanding is an input; market cap is the output.
A $500 stock with 1 million shares has a $500M market cap. A $50 stock with 100 million shares has a $5B market cap — 10× larger. Share price alone tells you nothing about company size.
Stock splits, buybacks (which reduce share count), new issuance from secondary offerings or employee grants, and reverse splits all change shares outstanding.
Basic shares are issued and held now. Diluted shares include potential dilution from options, warrants, and convertibles.
Related: Fully Diluted Market Cap