  Correlation studies of prompt and afterglow emissions from gamma-ray bursts
(GRBs) between different spectral bands has been difficult to do in the past
because few bursts had comprehensive and intercomparable afterglow
measurements. In this paper we present a large and uniform data set for
correlation analysis based on bursts detected by the Swift mission. For the
first time, short and long bursts can be analyzed and compared. It is found for
both classes that the optical, X-ray and gamma-ray emissions are linearly
correlated, but with a large spread about the correlation line; stronger bursts
tend to have brighter afterglows, and bursts with brighter X-ray afterglow tend
to have brighter optical afterglow. Short bursts are, on average, weaker in
both prompt and afterglow emissions. No short bursts are seen with extremely
low optical to X-ray ratio as occurs for "dark" long bursts. Although
statistics are still poor for short bursts, there is no evidence yet for a
subgroup of short bursts with high extinction as there is for long bursts. Long
bursts are detected in the dark category at the same fraction as for pre-Swift
bursts. Interesting cases are discovered of long bursts that are detected in
the optical, and yet have low enough optical to X-ray ratio to be classified as
dark. For the prompt emission, short and long bursts have different average
tracks on flux vs fluence plots. In Swift, GRB detections tend to be fluence
limited for short bursts and flux limited for long events.
