Answer:
No. A cashier's check is a check for which funds have already been collected by the guarantor (the bank who issues the cashier's check). They are purchased with cash or by immediate withdrawal from a depositor's account at that bank. Most people and businesses would prefer to receive a cashier's check than any other type of check.
A counter check is a check that is used when a depositor has no remaining pre-printed checks. It is given "over the counter", so to speak, at the bank when a depositor must write a check but has none left of their own. A counter check is a blank document on which the depositor's account number and name is hand-written or encoded by a bank officer. Many businesses will not accept counter checks.