To get to the -T6 temper, the 6061 is heated to about 990F, then quenched in water, then aged at about 350F for around 8 hours. That changes the typical yield strength from 8 ksi to about 40 ksi- fairly substantial.
But that quenching in water puts residual stresses in the aluminum, since there is a surface-to-center cooling gradient. The -T651 designation means the mill took that extrusion and gave it a 1% to 3% stretching, or permanent set, to get rid of some of those residual stresses.