A "spiral" and a "helix" are both technically spirals even though they each represent a different object. The two primary definitions of a spiral are as follows:

a. A curve on a plane that winds around a fixed center point at a continuously increasing or decreasing distance from the point.

b. A three-dimensional curve that turns around an axis at a constant or continuously varying distance while moving parallel to the axis.

The first definition is for a flat, often 2-Dimensional, planar curve that extends primarily in length and width, but not in height. A groove on a record or the arms of a spiral galaxy are examples of a spiral. The second definition is for the 3-Dimensional cylindrical variant of a spiral, called a Helix, that extends primarily in height. A spring (device) or a strand of a DNA are examples of a helix.

The length and width of a Helix typically remain static and do not grow like on a planar spiral. If they do, then the helix becomes a Conic Helix. You can make a conic helix with an Archimedean or equiangular spiral by giving height to the center point, thereby creating a cone-shape from the spiral.

In the side picture, the black curve at the bottom is an Archimedean spiral, while the green curve is a helix. A cross between a spiral and a helix, such as the curve shown in red, is known as a conic helix. The spring used to hold and make contact with the negative terminals of AA or AAA batteries in remote controls and the vortex that is created when water is draining in a sink are examples of a conic helix.