In the DS9 Technical Manual on page 14 under future advancements:
defensive shield impermeability. Total energy isolation is being studied as a subspace field generation method which allows no interaction between an established shield bubble and an outside force.
According to the TNG Technical Manual page 138, deflector shields are gravitational devices, that bend space around the ship, by passing gravitons through subspace field coils.
The warp drive is a propulsive phenomena that generates its field, by passing energized plasma through the subspace field coils. Furthermore on page 139:
Because of the spatial distortion inherent in the shielding generation process, there is a measurable effect on the geometry of the warp fields that propel the ship.
Both are different methods of creating subspace fields with different properties and effects.
A warp field, is propulsive and intended to lower the mass of the ship, being directed towards the ship, it would be quite useless as a shielding system other than by causing the incoming EM projectile to lose some of its energy due to a weak interaction.
A shield however is a static bubble directed outward from the ship and is therefore effective against incoming material, making it lose most of its energy, although there is always going to be some bleedthrough.
A warp field is not comparatively intense, and is directed towards the ship. A shield is intense, and is directed away from the ship. A warp field sits outside the shield bubble and will allow most energy to pass through it, the shield sits close to the hull and will not allow most energy through it.
Also according to page 138 of the TNG Technical Manual, the shield generators are rated for 473,000 MW per generator. By my calculations, a warp 1 warp field is only 1,000 MW.
Think of the shield as a ball of metal around the ship, and the warp field as a haze of heat and light beyond it.