Polymers were first classified according to polymerization method by Wallace Carothers in 1929, who introduced the terms addition polymer and condensation polymer to describe polymers made by addition reactions and condensation reactions respectively. However this classification is inadequate to describe a polymer which can be made by either type of reaction, for example nylon 6 which can be made either by addition of a cyclic monomer or by condensation of a linear monomer. 
Flory revised the classification to chain-growth polymerization and step-growth polymerization, based on polymerization mechanisms rather than polymer structures. IUPAC now recommends that the names of step-growth polymerization and chain-growth polymerization be further simplified to polycondensation (or polyaddition if no low-molar-mass by-product is formed when a monomer is added) and chain polymerization.
Most polymerizations are either chain-growth or step-growth reactions. Chain-growth includes both initiation and propagation steps (at least), and the propagation of chain-growth polymers proceeds by the addition of monomers to a growing polymer with an active centre. In contrast step-growth polymerization involves only one type of step, and macromolecules can grow by reaction steps between any two molecular species: two monomers, a monomer and a growing chain, or two growing chains. In step growth, the monomers will initially form dimers, trimers, etc. which later react to form long chain polymers.
In chain-growth polymerization, a growing macromolecule increases in size rapidly once its growth is initiated. When a macromolecule stops growing it generally will add no more monomers. In step-growth polymerization on the other hand, a single polymer molecule can grow over the course of the whole reaction.
In chain-growth polymerization, long macromolecules with high molecular weight are formed when only a small fraction of monomer has reacted. Monomers are consumed steadily over the course of the whole reaction, but the degree of polymerization can increase very quickly after chain initiation. However in step-growth polymerization the monomer is consumed very quickly to dimer, trimer and oligomer. The degree of polymerization increases steadily during the whole polymerization process.  
The type of polymerization of a given monomer usually depends on the functional groups present, and sometimes also on whether the monomer is linear or cyclic. Chain-growth polymers are usually addition polymers by Carothers' definition. They are typically formed by addition reactions of C=C bonds in the monomer backbone, which contains only carbon-carbon bonds. Another possibility is ring-opening polymerization, as for the chain-growth polymerization of tetrahydrofuran or of polycaprolactone (see Introduction above).
Step-growth polymers are typically condensation polymers in which an elimination product as such as HO are formed. Examples are polyamides, polycarbonates, polyesters, polyimides, polysiloxanes and polysulfones. If no elimination product is formed, then the polymer is an addition polymer, such as a polyurethane or a poly(phenylene oxide). Chain-growth polymerization with a low-molar-mass by-product during chain growth is described by IUPAC as "condensative chain polymerization".
Compared to step-growth polymerization, living chain-growth polymerization shows low molar mass dispersity (or PDI), predictable molar mass distribution and controllable conformation. Generally, polycondensation proceeds in a step-growth polymerization mode.