We investigate the structural and dynamical properties of counterion binding in sodium cholate and sodium deoxycholate micelles at three different concentration, namely, 30, 90, and 300 mM, by means of molecular dynamics simulations at the atomistic level. The obtained results can resolve a long-standing, apparent contradiction between different experiments that reported discordant values for the degree of counterion binding. Namely, our results suggest that certain experimental techniques, such as freezing point depression, are only sensitive to the contact counterions, and hence, the degree of contact binding of the counterions is measured. On the other hand, in experiments employing, e.g., electrode potential or nuclear magnetic resonance measurements, the solvent-separated counterions also contribute to the signal detected, and hence, the counterions that are measured as bound ones do include the solvent-separated counterions as well.