A helix is a curve in 3-d space with an axis, where the tangent line makes a constant angle with the axis. See here for some info on the helix. A circle would be the only helix which could lie in a plane, since the tangent line to a plane curve is always at 90 degrees from an axis normal to that plane. So a 2-d helix is not much of a helix, which more typically resemble corkscrews.
[Note: I take that back about plane curves --- the tangent line to any curve in the $xy$ plane (at any point on it) is at a 90 degree angle from the $z$ axis, so that any curve in the $xy$ plane would qualify as a helix under the constant angle definition. That makes such curves not good candidates for the term ""helix", i.e. the notion is trivially true for all plane curves.]
Spirals on the other hand do not need to have that property, and are typically curves in a 2-d plane. See the link here for some information about various types of spiral. Some of them are quite interesting.