terminology - What is the difference between depth of field and focal plane?

I would like to know how to address the difference between them and how relates to each other.

Answer

The focal plane is the distance from the camera at which the sharpest focus is attained. Depth of field is the range of distances either side at which the focus is "acceptably sharp".

The "acceptably sharp" part is what causes confusion as you need to make assumptions about viewing distance and visual acuity. For this reason a standard figure for the amount of blur that is acceptable tends to be used. It's thus important to realise that any depth of field numbers are approximate, suitable for comparison (i.e. this setup gives DOF of X meters, this setup gives DOF of Y meters) but the actual range that appears sharp will likely differ.

For lenses which exhibit a defect known as field curvature, the focal plane wont be flat but will curve outward, meaning when photographing something dead flat you could end up with the centre sharp but the corners out of focus.

Tilt-shift lenses allow you to tilt the focal plane relative the camera to better suit the subject (for example tilting the focal plane down would help you get more of the ground in focus).