Postgresql has some particular behaviour in regard to quoting and case sentivity: it folds every non-quoted identifier to lower case (also at creation time) and then works case-sensitively.
Double quotes in identifiers are only needed when the identifier (table name, column name, etc) was defined (at schema creation time) with uppercase letters (some or all) and between double quotes.
In that case (which I advice against), when you use that identifier, you must type it in the same way: case sensitively (type upper/lower case letter exactly as defined) and between double quotes.
In other cases, you can use non-quoted identifiers and work always case-insensitively.