What I said before applies specifically to what you were talking about earlier. In other words, when dealing with the dot product of two vectors in x,y,z coordinates the angle between the two is only dealing with the angle between them. This angle is only related to their separation along their mutual plane.

Three dimensional angles in general are a tougher concept altogether. You are now talking about a single vector in x,y,z and not a comparison between two. To be perfectly honest, I myself am not completely comfortable with this notion. From what I can remember though, this type of interpretation does rely on breaking down the xyz vector into two vectors in xy and xz. After this is done then the angle of separation between these two vectors is calculated.

Not too long ago we had an ongoing thread trying to detail the intracacies of steradians which are another interpretation of three dimensional angles. (They are strictly speaking square radians.) They are used by those who deal with three dimensional projections regularly. Perhaps this would be an informative study for you. I know it left me scratching my head for a while. I will mention that I did not find a direct relationship between steradians and normal two dimentional angles other than the strict definition of a steradian itself. Briefly, I know how they calculate the steradian, but I do not see the connection to two dimensional angles. Type steradian into your browser and do some reading on the subject and you will see what I mean.

Perhaps one of the more knowledgable members here can help you out more. Good luck.