Shareholders buy into a bank, and have a small say in how the bank is run.
Investors buy or invest in various types of bonds that the bank offers.
When you own a share (or shares) in a bank, you are a shareholder.
This means that you own a small piece of the bank, and you have a say in how the bank is run. You might even get to vote on important decisions (e.g. who sits on the banks board of directors).
Shareholders also have the potential to make money if the banks stock price goes up, because they can sell their shares for a higher price than they paid.
On the other hand, when you own a bond issued by a bank, you are a bondholder.
This means that you have lent money to the bank and the bank has promised to pay you back with interest. Bonds are a type of loan that investors make to companies, governments or other organizations.
The bondholder receives regular interest payments from the bank over a set period of time, and at the end of that period, the bank repays the initial amount of money that was borrowed.
Often the people buying shares or bonds are actually massive companies and not just an individual, but the principle holds true, they own a part of the bank.
The main difference then between a shareholder and a bondholder is just the type of ownership they have.