上記は全て選挙権を表します。特に意味に差異はありません。suffrageと言ったりもします。
ちなみに選挙権を持つようになる年齢をvoting ageといいます。
例
Japan is set to lower the voting age to 18 from 20.
日本は選挙権を持つ年齢が20歳から18歳に引き下げる予定です。
1. To cast a vote = A. To vote in an election. You seem happy about the results of the election. "I guess I know which candidate you cast your vote for! I need to go to the polling place and cast my vote!"
B. To share one's opinion on something (which could involve informal "voting").
"If I get a say in the matter, I cast my vote in favor of a new microwave for the break room! Raise your hand to cast your vote for lower monthly dues!"
To have a say = Also, have a voice in. Have the right or power to influence or make a decision about something. ...
Have one's say. Express one's views, as in:
"As soon as I've had my say I'll sit down."
Have the say. Be in command, as in:
"The general has the say over which troops will be sent."
1. To cast a vote =
A.選挙で投票すること。選挙結果に満足したのなら、
"I guess I know which candidate you cast your vote for! I need to go to the polling place and cast my vote!"
あなたがどの候補にいれたか知ってるよ！投票所にいって投票しなくちゃ！
B.考えをシェアする(カジュアルだが投票する意味も含む）
"If I get a say in the matter, I cast my vote in favor of a new microwave for the break room! Raise your hand to cast your vote for lower monthly dues!"
言わせてもらえるなら、休憩所の新しい電子レンジについて物も押したい。ひと月の料金が高すぎると思う人は手をあげてくれ！
To have a say = これは何か決定に関する権利や影響力がある、自分の言いたいことを言う、という時に使います。
Have one's say. Express one's views, とも使います。
例 "As soon as I've had my say I'll sit down."
Have the sayは命令権を持つという意味。
例："The general has the say over which troops will be sent."
In the UK, in 1918, all men over 21 and women over 30 won the right to vote. It wasn't until 1928 that all women over the age of 21 were also given the right to vote. In English, we call the long campaign for women to have the right to vote 'Suffrage', sometimes known as the 'Suffragette Movement'.
The right to vote is exercised by most citizens in America.
Voting rights for women were fought in the early 1900s.
Although voting is a right for American citizens, you are not required to exercise it.
Rights and the right to vote have been established
in most politically advanced countries. A fair voting
system where peoples rights can be expressed by
choosing to vote for their preferred political party or to form a
consensus on a subject.
In the UK we call this our right to vote
examples
"i am going to vote for my favourite party because
they represent my views".
or
I am exercising my right to vote"
Rights（権利）やthe right to vote（投票する権利）は政治先進国で確立されました。自分たちがより好む政党に投票したり、ある事柄について意見の一致をさせる時に選ぶことによって人々の権利が表現されるのが、公正な投票の仕組みです。
イギリスではこれをour right to vote（私たちの投票する権利）と呼びます。
例：
"i am going to vote for my favourite party because
they represent my views".（私は自分が1番好きな政党に投票します。なぜなら、彼らは私の価値観を代弁してくれているからです。）
あるいは
I am exercising my right to vote"（私は投票権を行使します。）
日本 
イギリス 
南アフリカ 
アメリカ合衆国 
