General terms:
* Rim: This is the most common and general term, referring to the top edge of the container.
* Lip: This term is used for the slightly raised edge that helps with pouring.
* Edge: This is a general term that can be used for any type of edge.
Specific terms for different shapes:
* Flange: This term is used for a wide, flat rim that helps to provide stability or support.
* Bevel: This term is used for a sloped edge that creates a smooth transition between the body of the container and the rim.
* Mouth: This term is often used for the opening of a bottle, which can also include the rim.
Other considerations:
* The specific term used may also depend on the material of the jar or glass. For example, a glass jar might have a "mouth" while a ceramic jar might have a "rim."
* The context of the conversation will also influence the most appropriate term. For example, if you're talking about pouring from a jar, you might say "the lip of the jar."
Ultimately, the best term to use will depend on the specific situation.