The electric and magnetic field vectors of a transverse electromagnetic wave are always at right angles to each other and in phase (for waves in a vacuum or non-conducting medium), whatever the state of polarisation. The polarisation state refers to the direction of the electric field vector, from which the magnetic field vector can always be inferred.
One way of thinking about polarisation is to note that it is always possible to deconstruct a transverse wave travelling in some particular direction into the sum of two separate components that are linearly polarised in orthogonal directions (e.g. see https://en.wikipedia.org/wiki/Polarization_(waves)#Polarization_state).
Thus we can construct a wave by adding two electromagnetic waves (of the same frequency and amplitude) but with the electric fields at right angles to each other and a common direction of wave motion.
If the two waves have zero phase difference, then they sum to give plane polarised light. The resultant electric field vector oscillates back and forth in a line at 45 degrees to the oscillation directions of the two contributing electric fields. This and the direction of wave motion defines a plane of polarisation.
If they have a phase difference of $\pm \pi/2$, then when they sum, the resultant E-field vector is of constant magnitude, but its direction rotates around. This is circularly polarised light. The tip of the resultant electric field vector draws out a circle when viewed along the direction of wave motion, or a helix when viewed in three dimensions, with its axis the direction of wave motion.
For an arbitrary phase difference the tip of the resultant electric field vector traces out an ellipse. i.e. Elliptically polarised light.
Play around with this Geogebra App that I wrote in order to model and explain this scenario. You can control the amplitude, frequency and phase difference of the two waves.