Carbonate esters have planar OC(OC)  cores, which confers rigidity.  The unique O=C bond is short (1.173 Å in the depicted example), while the C-O bonds are more ether-like (the bond distances of 1.326 Å for the example depicted).
Carbonate esters can be divided into three structural classes: acyclic, cyclic, and polymeric. The first and general case is the acyclic carbonate group.  Organic substituents can be identical or not.  Both aliphatic or aromatic substituents are known, they are called dialkyl or diaryl carbonates, respectively. The simplest members of these classes are dimethyl carbonate and diphenyl carbonate.
Alternatively, the carbonate groups can be linked by a 2- or 3-carbon bridge, forming cyclic compounds such as ethylene carbonate and trimethylene carbonate. The bridging compound can also have substituents, e.g. CH for propylene carbonate. Instead of terminal alkyl or aryl groups, two carbonate groups can be linked by an aliphatic or aromatic bifunctional group.
A third family of carbonates are the polymers, such as poly(propylene carbonate) and poly(bisphenol A carbonate) (e.g. Makrolon or Lexan).