Is there a specific term for reactions of the form A + B → C + D?
There are 4 'base-types' of chemical reactions:


Synthesis reactions ($\ce{A + B -&gt; AB}$)
Decomposition reactions ($\ce{AB -&gt; A + B}$)
Substitution reactions ($\ce{A + BC -&gt; B + AC}$)
Metathesis reactions ($\ce{AB + CD -&gt; AD + CB}$)


Given that you talk about polymers that in one case combine to form a new (single) polymer: $\ce{A + B &lt;=&gt; C}$ you could call this a synthesis reaction.

You other example, $\ce{A + B &lt;=&gt; C + D}$, is an exchange of parts of the polymers so that would be a metathesis reaction.

For polymers there are a couple of additional options to name the types of reactions, but these depend a lot on the specific chemistry (e.g. hydrolysis if water is one of the reactants) so that is probably difficult if you have 'abstract' polymers.