I looked it up and I'm still confused. Apparently, sieve cells lack sieve plates? What does that really mean? It's difficult to find a good picture of either.
All plants have sieve cells, but not all plants have sieve tube elements because they evolved after the plant family tree had started to branch. Only angiosperms have sieve tube elements.
Sieve tube elements are more specialized for their job as transport cells, and can transport more nutrients faster than sieve cells. During their development, the meristem cell divides into two cells: the sieve tube element and the companion cell. The sieve tube element loses its nucleus, vacuoles, and ribosomes when it matures in order to make it easier for its cytoplasm to flow, and so it relies on its companion cell for proteins and carbohydrates. The porous plates between sieve tube elements provide little resistance to water and nutrient flow, and so flow through the sieve tube is more rapid than it would be if there were cell membranes or small pores for it to pass through. The sieve tube elements are wide to make wide tubes, which provide less resistance to fluid flow.
Sieve cells evolved before sieve tube elements, and are a bit less specialized for their job. They still have all their organelles, and are long and thin. Some plants, such as seedless plants and gymnosperms, don't have any sieve tube elements and rely solely on sieve cells for nutrient transport.