RE: Bezier vs Spline
google, wikipedia, and the terms bezier, spline, NURBS, and b-spline should get you started.
some terms to look out for: uniform, interpolated, natural.
interpolated means that a point is specified which the curve must pass through.
a bezier curve is a third order polynomial function with 4 "handles" - 2 interpolated endpoints and 2 that control curvature. bezier splines are multiple bezier curves which are tangent across each interpolated endpoint.
NURBS curves (Non Uniform Rational B-Spline) are what Autocad calls a spline. NURBS splines (yes thats redundant) allow for an extra few variables, including how interpolated each endpoint should be. this means that you can make a spline that fits more smoothly and isnt tied to exactly what data points you've picked. this is controlled by a variable called "fit tolerance" in autocad, and is a unitless number from 0 to 1, where 0 is fully interpolated.
B-splines is short for Basis splines, which is confusing but does not mean Bezier Spline.
Natural splines imply the condition that endpoints have a zero second order derivative. This means that they are the local maximum or minimum between critical points (which are the points where the first-order derivative equals zero).
I've seen someone say that splines *shouldnt* be used to draw airfoils. I think what he means is that for an airfoil to be true to its data set, it should be drawn with an interpolated line.
-Barrett