A <monomer> is a <chemical substance> whose <molecules> can undergo <polymerization> and contribute units to the essential structure of a <polymer>. A <monomer molecule> is the individual reactant; its incorporated <monomeric unit> is the portion identifiable as derived from that reactant. Incorporation can change <chemical bonds> and release small byproducts, so the unit in the chain need not have the complete <molecular formula> of the feed <molecule>. See https://old.goldbook.iupac.org/html/M/M04019.html[IUPAC: monomer molecule] and https://doi.org/10.1515/pac-2023-0304[IUPAC, A brief guide to polymer terminology: monomeric units].

Three different counts answer three different questions. <Monomer molecules> describe the feed; <monomeric units> trace that feed's contributions to the product; a <constitutional repeating unit> describes the smallest chemical pattern repeating along a regular chain. In <Nylon 6,10>, two different <monomers> supply one interior <constitutional repeating unit>,
$$
\mathrm{{-}NH{-}(CH_2)_6{-}NH{-}C(=O){-}(CH_2)_8{-}C(=O){-}}.
$$
Its <molecular formula> is $\mathrm{C_{16}H_{30}N_2O_2}$. The diamine feed is $\mathrm{C_6H_{16}N_2}$, and the diacid-chloride feed is $\mathrm{C_{10}H_{16}Cl_2O_2}$; subtracting two $\mathrm{HCl}$ gives the interior-repeat budget. For a finite linear chain made from $n$ of each reactant, there are $2n-1$ joining connections, hence $2n-1$ formal $\mathrm{HCl}$ eliminations, rather than $2n$. One <amine> end and one acid-chloride end remain in that ideal unmodified chain. This is a <stoichiometry> check on the depicted reaction, not a claim that the washed experimental thread retains those ends. The reacting end-group chemistry is documented in https://ocw.mit.edu/courses/10-569-synthesis-of-polymers-fall-2006/d9f9ac7021b0d0f418d3d3c90dbfb94b_lec05_09152006.pdf[Hammond, lecture 5, p. 4]; the specified <Nylon 6,10> reactant pair is reported in https://pubs.acs.org/doi/10.1021/acs.jchemed.6b00767[Polymer Day, nylon demonstration].

<Ethene> shows the reverse counting mismatch. One $\mathrm{CH_2{=}CH_2}$ <monomer molecule> contributes a two-<carbon> $\mathrm{{-}CH_2{-}CH_2{-}}$ <monomeric unit> to ideal linear <polyethylene>, without a small byproduct in that growth step. But the smallest <constitutional repeating unit> of its uniform backbone is just $\mathrm{{-}CH_2{-}}$: a chain containing $m$ incorporated <ethene> <monomeric units> contains $2m$ such interior one-<carbon> repeats. End groups are additional bookkeeping. The frequently drawn $[\mathrm{{-}CH_2{-}CH_2{-}}]_m$ is useful for tracing the feed, although it is not the smallest constitutional repeat. The minimum-pattern definition is given in https://goldbook.iupac.org/terms/view/C01286/plain[IUPAC: constitutional repeating unit]; the <ethene> growth chemistry is described by <Organic Chemistry by John McMurry/31.1 Chain-Growth Polymers>[McMurry, Organic Chemistry, 31.1]{ref}.

A segment of a <freely jointed chain> or <Gaussian chain> instead belongs to a statistical model. It can represent many <chemical bonds> and several <constitutional repeating units>; its length and the segment count are chosen to describe chain conformation at the intended scale. The three-repeats-per-segment drawing in <polymerization monomers interface units> is a deliberately arbitrary coarse-graining example, not a measured <Kuhn length>. Always state the counting convention before substituting a segment count for a <degree of polymerization>. This separation lets chemistry track which <chemical atoms> entered the material while statistical models track how the material bends and extends.


 Monomer (source code)