There are 3 common types for spline:

1. Parallel key spline (Rectangular spline)

where the sides of the equally spaced grooves are parallel in both directions, radial and axial.

2. Involute spline

where the sides of the equally spaced grooves are involute, as with an involute gear, but not as tall. The curves increase strength by decreasing stress concentrations.

Parallel Key Spline and Involute Spline
Parallel Key Spline and Involute Spline

3. Helical spline

where the equally spaced grooves form a helix about the shaft. The sides may be parallel or involute. This can either minimize stress concentrations for a stationary joint under high load, or allow for rotary and linear motion between the parts.

Corresponding to the spline, spline shafts have the types of rectangular spline shaft and involute spline shaft.

Involute Spline Shaft
Involute Spline Shaft

Spline joint is a combination with internal spline and external spline. For instance, a gear mounted on a shaft might use a external spline on the shaft that matches the internal spline on the gear.

Rectangular Spline Joint
Rectangular Spline Joint