'Special postgres operators

From the docs on Operators, it says:

An operator is a sequence of up to NAMEDATALEN-1 (31 by default) characters from the following list:

+ - * / < > = ~ ! @ # % ^ & | ` ? $

I've familiar with the more standard arithmetic and bitwise operators, but what are the following operators in Postgres?

! (is this just when doing not equals checks -- this != that ?
@
` (how does backtick work? I've used it in MySQL to quote fields, but never in Postgres)
$
#

postgresql

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