Generally distinct types of unsaturated organic compounds are recognized.  
For hydrocarbons:
*alkene (unsaturated) vs alkane (saturated)
*alkyne (unsaturated) vs alkane (saturated)
*arene (unsaturated) vs cycloalkane (saturated)
For organic compounds containing heteroatoms (other than C and H), the list of unsaturated groups is long but some common types are:
*carbonyl, e.g. ketones, aldehydes, esters, carboxylic acids (unsaturated) vs alcohol or ether (saturated)
*nitrile (unsaturated) vs amine (saturated)
*nitro (unsaturated) vs amine (saturated)
Unsaturated compounds generally carry out typical addition reactions that are not possible with saturated compounds such as alkanes. A saturated organic compound has only single bonds between carbon atoms. An important class of saturated compounds are the alkanes.  Many saturated compounds have functional groups, e.g., alcohols.