Blackmail (noun) is the action of demanding money from a person in return for not revealing personal information that would hurt the individual. Blackmail can also be a verb.
To coerce (verb) someone is to persuade them to do something by using force or threats, or to obtain something by the use of force or threats.
Typically, to blackmail someone implies that you have a piece of information about them, which you are using to get the person to do something for you. To coerce someone, alternatively, is to make someone do something by use of threat (ie threatening that you would hurt someone's family in a vague way). You could use blackmail to coerce someone into doing something.