Suffrage, franchise, vote, ballot mean the right, privilege, or power of expressing one’s choice or wish (as in an election or in the determination of policy).
Suffrage is the usual term when the emphasis is upon the extent to which this privilege or power is enjoyed in a state or community or upon the kinds of citizens in a representative government who legally exercise this power; the word is frequently modified by a term indicating such extent or restriction.
Franchise may be chosen when the privilege or power is thought of as conferred by the government or as a statutory or legal right.
Vote is appropriate when the stress is on the power of each of the individuals on whom the franchise has been conferred to express his choice or opinion in the approved way, thereby aiding in the task of determining the will of the people.
Ballot , which specifically implies some method of secret voting, is likely to be used when the emphasis is on the power to vote freely, effectively, and without coercion, on the expressed will of the majority, or on the ethical use of the vote.