Addition polymerization and condensation polymerization are two distinct processes by which monomers combine to form polymers, each with unique characteristics.

Addition Polymerization
In addition polymerization, monomers join together through a series of repeated addition reactions without the loss of any small molecules. This process occurs primarily with unsaturated monomers, such as ethene ($C_2H_4$) and propene ($C_3H_6$), which react to create long chains of saturated polymers. Importantly, the resulting polymer retains the same molecular formula as the original monomer. For instance, when ethene undergoes addition polymerization, the resulting polymer, polyethene, has the general formula $C_nH_{2n}$, where $n$ represents the number of repeated units.

Condensation Polymerization
In contrast, condensation polymerization involves the joining of monomers with the concurrent loss of small molecules, such as water ($H_2O$) or hydrogen chloride ($HCl$). This process typically occurs when two different types of monomers, such as amino acids or diols and dicarboxylic acids, react to form a polymer. As these monomers link together, a small molecule is eliminated, resulting in a polymer that has a different molecular formula from that of the starting monomers. For example, when a diol reacts with a dicarboxylic acid, the condensation reaction yields a polyester and releases water as a byproduct.

Functional Groups
Another significant difference between these two polymerization processes lies in the types of functional groups involved. Addition polymerization requires unsaturated monomers, which contain double or triple bonds that can participate in the reaction. On the other hand, condensation polymerization involves monomers with specific functional groups that can react with each other, such as hydroxyl ($-OH$) and carboxyl ($-COOH$) groups.

Conclusion
In summary, addition polymerization is characterized by the joining of monomers without the loss of small molecules, while condensation polymerization results in the elimination of small molecules during the reaction. The types of functional groups involved and the different molecular formulas of the resulting polymers further distinguish these two processes.