Whether a menu button or disclosure button should be used depends on the type of content that is revealed when the button is pressed. From W3C: "A menu button is a button that opens a menu. It is often styled as a typical push button with a downward pointing arrow or triangle to hint that activating the button will display a menu."
Typically, a disclosure buttons are informational as they control the visibility of content and reveal content once activated.
For example: If there is an FAQ section within your site and the questions are interactive components that, when pressed, reveal the answer to the question, it would be appropriate to code this content as a disclosure button.
To ensure custom widgets are properly communicating their names, roles, states, values, and properties with users, including users of assistive technologies, the Guided Manual WCAG Audit Tool from Accessible Web includes steps on how to adhere to the ARIA Design Pattern Specifications.