What is the difference between shares, stock and stakes?

Shares are the individual units of ownership of a company. The total number of shares of a company is somewhat arbitrary and can be changed by splits. A company worth $1 billion might be divided into 10 million shares worth $100 each, or 100 million shares worth $10 each. Professional trading is typically done in "lots" of 100 shares; individuals can own as little as 1 share or in some cases even fractional shares.

Stock is the general term for the instrument of partial ownership of a company. An amount of stock is measured in shares, just as an amount of money is measured in dollars or euros or whatever. "A stock" is the stock of a particular company. If you own 100 shares of Microsoft, you don't own 100 stocks; you own 100 shares of 1 stock. However, by metonymy, "stock" and "share" are sometimes used interchangeably in general terms. For example, "stockholder" and "shareholder" mean the same thing. And what Americans call "stock market" and "stock trading", others may call "share market" and "share trading".

Stake also refers to partial ownership of a company, but measured as a fraction of the entire company. For example, if someone owns a 10% stake in Microsoft, it means they own 10% of all outstanding shares.