Sharpness and "crispness" are related, but they're not identical (at least in the language of critique).
Sharpness is an evaluation of how well the detail in the image is recorded; crispness is about how well that detail is conveyed to the viewer. A crisp image will be sharp (mostly, that is, where sharpness counts), but it will also necessarily have a degree of contrast (at several levels) that allows the viewer to notice that it's sharp.
Straight out of camera, the difference between merely sharp and crisp could come down to a simple difference in lighting, with all other factors (lens, overall exposure, aperture, focus distance, focus accuracy, etc.) being the same — a picture taken under very flat light will not have nearly the same ability to convey apparent detail, texture and shape as an otherwise identical picture taken under slightly contrastier lighting conditions. Put both pictures on screen at a ridiculously high magnification, though, and you will see that the same size of details are recorded in both.
A beginning or casual photographer is at a distinct disadvantage here. Their camera will produce absolutely stunning images sometimes, and, well, duds at other times, using the exact same settings (where, admittedly, "the exact same settings" may simply mean "it was on 'P' for 'Professional'" or some other automated setting, with the same JPEG/rendering preset selected). Without some appreciation of lighting (both quality and direction) and some basic understanding of how to finish the picture (whether that means post-processing or simply selecting a different picture style on the camera, one that's more appropriate to the conditions), the photographer is at the mercy of circumstance, and the camera takes both the credit for successes and the blame for failures.
Provided that the camera and lens (and tripod, where applicable) are capable of rendering sharp images, the photographer can create crisp images. Or not.