Try looking under plug or slot welds.  The AISC Manual has charts as well, page 4-155 in the ASD 9th, 8-31 in the LRFD 3rd.  Basically you replace the fillet weld triangle with a small rectangle.

I believe puddle welds are different from plug or slot welds.  Plug or slot weld is connecting two plates with one plate having either a round hole or a slotted hole.  Puddle weld is in a case where say you are attaching a metal deck to a steel beam.

Old AWS used to have a symbol for spot or projection weld (which may or may not be in the new AWS).  Symbol is a small circle drawn on the arrow side (if it matters) or a small circle centered about the reference line if the side doesn't matter.  You indicate the diameter of the weld and the center to center spacing.

Typically, I do not see this weld symbol anymore.  Puddle welds are specified more often in a note or within a schedule.

"Puddle weld.  A nonstandard term for an arc spot weld or plug weld."- from "Standard Welding Terms and Definitions".

"Plug or slot weld" symbol is a rectangle on the weld arrow.

"Spot or projection" is a circle, either tangent to the weld arrow or centered on the weld arrow when there is no "side" significance.

From "Standard Symbols for Welding, Brazing and Nondestructive Examination".

It is interesting that a nonstandard term is so widely used in the industry.

I can't recall any other "structural application" of a puddle weld other than in metal deck attachment in conjunction with SSW, TSW or BP.