We examine the tangential magnetic field and velocity shears across directional discontinuities (DDs) with significant change in magnetic field intensity observed by WIND in slow and fast solar wind streams. The magnetic field rotation sense in fast wind DDs is that predicted by theory for outward propagating rotational discontinuities (RDs), but flow shear magnitude and orientation do not always satisfy RD theory. Alternatively, DDs with small normal magnetic field can be regarded as tangential discontinuities (TDs); the observed shears imply that the length scale over which the proton velocity distribution changes at the discontinuity can be both smaller or larger than that of the electron distribution. The slow wind includes a larger fraction of DDs that disagree with RD theory. It is shown that the flow shear orientations allowed in a TD provide a continuous transition between the opposite orientations for RDs propagating along or against the magnetic field direction.