According to AWS A3.0-94 Standard Welding Terms and Definitions
"
Stringer bead. A type of weld bead made without appreciable weaving motion. See Figure(22A)"... which basically shows a butt joint where the bead is made in a straight continuous motion with forward progress along the joint.
"
Weave bead. A type of weld bead made with transverse oscillation. See Figure (22B)"... which shows a butt joint where the bead is made with a side to side motion as forward progress along the joint was made.
I agree with cccasey in his description of the two beads in that most people define them as he did in reference to the ratio of the bead width to the diameter of the electrode.
John Wright