Final answer:
The feature with both a button and an arrow for a drop-down list in Microsoft Office is a split button, such as the Font Color button in Word.
Step-by-step explanation:
The feature described in the question is commonly found in the user interface of Microsoft Office applications like Word, Excel, and PowerPoint. Typically, this feature consists of a split button where one part is a button that, when clicked, applies a default or last-used feature.
Beside it is a small arrow that, when clicked, displays a drop-down list of additional options or variations of the feature to choose from. An example of this in Microsoft Word is the Font Color button, where clicking the left side applies the last-used color, and clicking the arrow on the right displays a palette of other colors you can select.