  We study the crossover between thermodynamic Casimir forces arising from
long-range fluctuations due to Goldstone modes and those arising from critical
fluctuations. Both types of forces exist in the low-temperature phase of O$(n)$
symmetric systems for $n>1$ in a $d$-dimensional ${L_\parallel^{d-1} \times L}$
slab geometry with a finite aspect ratio $\rho = L/L_\parallel$. Our
finite-size renormalization-group treatment for periodic boundary conditions
describes the entire crossover from the Goldstone regime with a nonvanishing
constant tail of the finite-size scaling function far below $T_c$ up to the
region far above $T_c$ including the critical regime with a minimum of the
scaling function slightly below $T_c$. Our analytic result for $\rho \ll 1$
agrees well with Monte Carlo data for the three-dimensional XY model. A
quantitative prediction is given for the crossover of systems in the Heisenberg
universality class.
