Molecular dynamics simulations were used to study the structural and dynamical properties of a water-like core-softened fluid under confinement when the confining media is rigid or fluctuating. The fluid is modeled using a two-length scale potential that reproduces, in the bulk, the anomalous behavior observed in water. We perform simulations in the NVT ensemble for fixed flat walls and in the NpT ensemble using a fluctuating wall control of pressure to study how the fluid behavior is affected by fixed and non-fixed walls. Our results indicate that the dynamical and structural properties of the fluid are strongly affected by the wall mobility.