is "executive" a well defined term for american corporate law? like "a person who can allocate funds from the master bank account without approval" or something like that?

generally unilateral decision making (up to a point) + supervisory functions of an entire group / department / vertical

e.g. they own all of Finance (or Ops, or Legal, or whatever), and have the ability to hire, fire, and use their own budget, albeit it with strings.

"Officer" is typically anyone who can bind the company contractually.

Not really, It's just another term for upper management. It's just shorthand for any employee whose title begins with "Chief" or has "Executive" in it (among others like Chairman, President, etc).

Usually, people who can make large decisions for the business without approval from higher-level employees.