The process of magnetic reconnection when studied in Nature or when modeled in 3D simulations differs in one key way from the standard 2D paradigmatic cartoon: it is accompanied by much fluctuations in the electromagnetic fields and plasma properties. We developed a diagnostics to study the spectrum of fluctuations in the various regions around a reconnection site. We define the regions in terms of the local value of the flux function that determines the distance form the reconnection site, with positive values in the outflow and negative values in the inflow. We find that fluctuations belong to two very different regimes depending on the local plasma beta (defined as the ratio of plasma and magnetic pressure). The first regime develops in the reconnection outflows where beta is high and is characterized by a strong link between plasma and electromagnetic fluctuations leading to momentum and energy exchanges via anomalous viscosity and resistivity. But there is a second, low beta regime: it develops in the inflow and in the region around the separatrix surfaces, including the reconnection electron diffusion region itself. It is remarkable that this low beta plasma, where the magnetic pressure dominates, remain laminar even though the electromagnetic fields are turbulent.