The shape of a diamond refers to its profile, while the cut is more specific than that and is used to allude to the shape, number and even alignment of its facets. Round brilliant is the most popular cut diamond option for engagement rings. The traditional cut maximizes the sparkle of a diamond, surpassing that of other cut gemstones.
An oval cut diamond is popular too, although not as popular as one with a round cut. Still, there are many other types of diamond cuts, derived from the oval shape, such as marquise, pear, and heart, and those are quite fashionable. While a marquise cut diamond feature two sharp ends, one with pear cut features a sharp end; heart cut diamond is an oval cut gem with a sharp end as well as a cleft.
Rectangular diamond cuts are also getting popular these days, especially the princess, the emerald, the radiant, and the Asscher cut. If that is the shape you prefer, then look for a princess cut diamond ring, as that is the most popular rectangular option.