We present simultaneous two-dimensional measurements of the velocity and buoyancy fields on a central vertical plane in two-dimensional line plumes: a free plume distant from vertical boundaries and a wall plume, adjacent to a vertical wall. Data are presented in both an Eulerian and a plume coordinate system that follow the instantaneous turbulent/non-turbulent interface (TNTI) of the plume. We present measurements in both coordinate systems and compare the entrainment in the two flows. We find that the value of the entrainment coefficient in the wall plume is greater than half that of the free plume. The reduction in entrainment is investigated by considering a decomposition of the entrainment coefficient based on the mean kinetic energy where the relative contributions of turbulent production, buoyancy and viscous terms are calculated. The reduced entrainment is also investigated by considering the statistics of the TNTI and the conditional vertical transport of the ambient and engulfed fluid. We show that the wall shear stress is non-negligible and that the free plume exhibits significant meandering. The effect of the meandering on the entrainment process is quantified in terms of the stretching of the TNTI where it is shown that the length of the TNTI is greater in the free plume and, further, the relative vertical transport of the engulfed ambient fluid is observed to be 15 % greater in the free plume. Finally, the turbulent velocity and buoyancy fluctuations, Reynolds stresses and the turbulent buoyancy fluxes are presented in both coordinate systems.