What is the difference between uniqe index/unique/unique key/unique constraint keywords?
There are no differences between all the SQL statements, except the third one you're using a different name for the unique index, that's all.

All of them creates a unique key/index, constraint md5_constraint unique (query_md5) has the same effect.

Just pick the name you prefer for the unique key and feel free to use any of your queries. :)