  We use Brownian dynamics simulations and analytical theory to compare two
prominent types of single molecule transitions. One is the adsorption
transition of a loop (a chain with two ends bound to an attractive substrate)
driven by an attraction parameter $\varepsilon$, and the other is the
loop-stretch transition in a chain with one end attached to a repulsive
substrate, driven by an external end-force $F$ applied to the free end.
Specifically, we compare the behavior of the respective order parameters of the
transitions, i.e., the mean number of surface contacts in the case of the
adsorption transition, and the mean position of the chain end in the case of
the loop-stretch transition. Close to the transition points, both the static
and the dynamic behavior of chains with different length $N$ are very well
described by a scaling Ansatz with the scaling parameters $(\varepsilon -
\varepsilon^*) N^\phi$ (adsorption transition) and $(F-F^*) N^\nu$
(loop-stretch transition), respectively, where $\phi$ is the crossover exponent
of the adsorption transition, and $\nu$ the Flory exponent. We show that both
the loop-stretch and the loop adsorption transitions provide an exceptional
opportunity to construct explicit analytical expressions for the crossover
functions which perfectly describe all simulation results on static properties
in the finite-size scaling regime. Explicit crossover functions are based on
the Ansatz for the analytical form of the order parameter distributions at the
respective transition points. In contrast to the close similarity in
equilibrium static behavior, the dynamic relaxation at the two transitions
shows qualitative differences, especially in the strongly ordered regimes.
