Neat

From Wikipedia:

There is substantial confusion in the usage of "neat", or "straight up", "straight", and "up". In the context of describing ways of serving a drink, all of these mean "served without ice", but some bar patrons and bartenders use them inconsistently.

"Neat" and "up" are relatively unambiguous. The term "neat" means "a single, unmixed liquor at room temperature", and "up" means "chilled and served without ice in a cocktail glass".

"Straight" is often used interchangeably with "neat" (in the United Kingdom, Canada, and the United States). However, "straight" is also often used to refer to a spirit that is in an unmixed state in general, in addition to being used to describe a way of serving it. For example, many bourbons are identified as "Kentucky straight bourbon whiskey" on their bottling labels, and U.S. Federal law contains a legal definition of the term "straight whiskey". So sometimes "straight" may be used to mean either "straight up" (as defined above) or "neat", and clarification may be needed to determine the exact manner for serving it.

"With a twist" signals the bartender to add a "twist" of lemon or lime (bar choice, if unspecified) to the cocktail. Often, the bartender will hang the rind of the citrus on the glass as a garnish.