Draw is considered the action of the strop, or the feel of drag across the leather. The heavier the dragging feel = heavy draw. Some feel that a heavy draw produces more friction on the edge, therefore producing a keener feeling edge. Or something like that

. Either way, with all due respect to Larry's poor man strop, your new strop is of superior quality and likely produced a better stropped blade. So in a way it WAS the strop, but it was your technique that resulted in razor burn, not the strop itself. The only way I can really explain the differences is by comparing the result you would get stropping off an old leather belt vs a proper strop like an SRD.
I should apologize for my use of Razornese. We sometimes forget that new guys don't know the lingo yet.