As the above post says, Bernoulli is the equation that relates velocity to pressure, whereas Magnus Effect is a synonym for lift created when a ball or cylinder rotates in a freestream. Friction on the surface of the ball or cylinder grabs a little air from one side and dumps it on the other, while accelerating the air on the other side. This difference in velocities from one side of the ball to the other produces a change in pressure on each side, a la Bernoulli.
Think of the term "Magnus Effect" as a synonym for the word "lift" but applying only to balls and cylinders. Don't get hung up on it. They only use the Magnus Effect as a teaching tool because it is a good way to introduce basic concepts of lift. It stems from the old hydrodynamic theory that preceded modern aerodynamic theory. When the same freestream is combined with the circulation-causing effects of a wing you get lift, but since it is a wing you do not call it Magnus Effect.
The basic idea is that when you combine the velocity of a freestream with the tendency of body to wrap air around itself, lift is the byproduct. The reason they don't just use a wing to show this is that if you look at a correct streamline drawing of a wing in operation, air breaks off right at the trailing edge, which is confusing when you want to see how circulation generates lift since there is no circulation at the back. Air cannot turn the corner at the back edge fast enough to do so, while a ball or cylinder allows the air to go all the way around as there are no sharp edges.
Airplanes can in fact use rotating cylinders to create lift, and there have been some designs that used them. They are not very flexible in terms of flight speed and they create other problems for the aircraft.
wikipedia
Magnus Effect