The single word exposure gets tied to a variety of different intended meanings. Distinguishing between exposure and Exposure Value (EV) is a good step toward better clarity in terminology. A few more suggested distinctions, which may offer some additional descriptive clarity, are between the terms exposure, exposure level, and exposure control. There are a variety of light sensitive imaging systems which may utilized, each containing a recording medium for capturing images.
In photographic terms, Exposure is an event which produces a quantity of light onto a light sensitive surface over a period of time. Exposure Level is the effect that an exposure event has on a light sensitive medium which can be measured and recorded. Exposure Control is the balancing of the input level of light with the sensitivity level of the recording medium to achieve the desired tonality and other qualities of an image. Accurate exposure control is necessary to record the range of desired brightness levels in a scene and balance tonality effectively in the image you envision and intend to produce.
Despite our best efforts at exposure control, or those of a camera's auto exposure system, we may have an imbalance among the variables which results in a poorly recorded image. The exposure value chosen may produce scene brightness levels which are higher or lower than you desire for the recording medium. This may result in the range of recorded brightness levels being too high or low to be considered either optimal or within your tolerance for deviation from your quality standards. In the photography world, these poor quality results are referred to as overexposure and underexposure. There are a variety of potential remedial actions within the imaging chain which may improve the result, but those are separate from the terms which have long been applied in describing images which exhibit undesirable brightness and tonality characteristics in their recorded representation of a scene.