Even though the three-dimensional static organization of chromatin is highly studied, chromatin is a dynamic structure, and time-dependent changes are crucial for biological function. While it is known that both intra-chromatin interaction and loop extrusion are crucial to understanding chromatin organization, what is their respective role in deciding the nature of spatial and temporal organization is not clear. Simulating a model with active loop extrusion and intra-chromatin interactions, we show that under certain conditions, the measurable dynamic quantities are dominated by the loop extrusion, even though the population-averaged contact map (structure) can be dominated by intra-chromatin interactions, with loop extrusion playing no major role. Our results show that the dynamic scaling exponents with loop extrusion are consistent with the experimental observations and can be very different from those predicted by existing fractal-globule models for chromatin. We argue that one needs to measure both the structure and dynamics simultaneously to unambiguously interpret the organization of chromatin.