A depositor is someone who deposits money with a bank. Typically, when you deposit a sum of money with a bank, that bank owes a debt to you for an amount equal to that sum.
A creditor is someone to whom others owes a debt (for instance, if A takes out a $10 loan from B, then B is a creditor of A).
Bail-outs and bail-ins are two methods of rescuing financial institutions when they are distressed (e.g. during a financial crisis). They are not mutually exclusive, but nations typically elect to implement one or the other as their primary response to financial crises.
Bail-outs involve governments providing assistance to financial institutions when they are at risk of failing. They typically include measures such as subsidies; the provision of low-interest loans by central banks; and the purchase and insurance of toxic assets by governments. An example of a bail-out is the US$700bn bailout package provided by the US Treasury to failing banks during the 2008 Financial Crisis.
Bail-ins, on the other hand, aim to assist at-risk financial institutions by using the money of their creditors, depositors and shareholders. They typically involve measures such as: Writing down or cancelling debts owed by financial institutions to their creditors and depositors; converting some debts owed by financial institutions into equity (e.g. shares) in those institutions, thereby diluting the value of pre-existing shares; and/or cancelling some shares in financial institutions.
Bail-ins were used to rescue banks in Cyprus during the 2012-13 Cypriot financial crisis. Following the passing of the Dodd-Frank Act in 2010, they now also form part of the default measures to be used in the United States in the event of a financial crisis.