A bunch of this is 'it depends,' which makes single cheat sheets hard. Backticks in MySQL and BigQuery denote identifiers, like mutli-word table names. T-SQL uses squarebrackers for the same, and PostgreSQL wraps the same in double quotes.

If the SQL dialect doesn't use one of single or double quotes for something else, they are probably interchangeable for strings.

As for cases, the SQL syntax IS NOT case sensitive (in most cases?) and whether table names are or are not case sensitive will come down to the underlying operating system (or flavour of SQL) - servers on a *nix environment will have case sensitive names, because their underlying file structures are case sensitive. Microsoft SQL is (generally?) not case sensitive, because windows doesn't care.

..but that doesn't mean strings are or aren't case sensitive on those platforms, because that is dictated by the text collation being used.