TL;DR: No, not always, but most of the time.
Well, most planets are in either an equatorial orbit (~0° in relation to the star's rotation vector / equator). Some are in polar orbit (~90° and almost perpendicular to the star's equator/rotation vector), and even fewer are in retrograde or strange (highly eccentric or inclined) orbits. For example, all the major planets in our Solar System orbit the Sun in an equatorial orbit. WASP-79b, a hot Jupiter, orbits in a near polar orbit (deviation of 5°). WASP-17b and HAT-P-7b are both in retrograde and highly inclined orbits to their parent stars. Neptune's moon, Triton, orbits in an inclined, retrograde orbit, suggesting that Triton may be a captured body (but that is a long story that is unrelated). This means that a planet's orbit does not necessarily, have to align with the parent star's rotation vector.