Which term would best describe music played 'with a smooth and connected style'?

The term that best describes music played "with a smooth and connected style" is legato. This term indicates that the notes should be played without any noticeable breaks between them, creating a seamless and fluid musical line. When a melody is performed legato, it enhances the expressiveness and lyrical quality of the music, allowing for a flowing interpretation that connects each note to the next.

In contrast, other terms have different meanings that do not align with the idea of a smooth connection. Staccato refers to a style where notes are played sharply and detached from one another, creating a distinctly separated sound. Cantabile indicates a lyrical and song-like manner of playing but doesn't specifically mandate the smooth connection inherent in legato. Con brio conveys a sense of vigor and spirited energy but lacks any reference to smoothness or connectedness in the style of play. Thus, legato is the most appropriate choice for conveying a smooth and connected style in music performance.