Parallel-plate capacitor

That first sentence is close to EK 10.6.A.1 in AP Physics 2 and EK 10.3.A.1 in C: E&M, which agree word for word on the definition. What earns the shape its own name is the field it makes.

Uniform field. EK 10.6.A.3 says the field between two charged parallel plates with uniformly distributed charge is constant in both magnitude and direction, except near the edges. The AP Physics 2 sheet prints its magnitude as

C: E&M reaches the same expression with $\kappa = 1$ by applying Gauss's law and the principle of superposition, printing $E = Q/(\varepsilon_0 A)$ as a derived equation at EK 10.3.A.3.i, and EK 10.3.A.3.ii adds that the field is proportional to the surface charge density on either plate.

A charged particle inside behaves like a projectile. Constant field means constant force means constant acceleration, so EK 10.6.A.3.ii points you straight at projectile motion with the field playing the role of gravity.

Scope. AP Physics 2 requires only parallel-plate capacitors and ignores edge effects unless a question says otherwise. C: E&M adds concentric spherical and coaxial cylindrical ones. Both sheets set $\kappa = 1.0$ by convention unless a dielectric is stated.

The ratio $C = Q/\Delta V$ and the geometry formula belong to capacitance.