Withholding of removal is similar to asylum, but it does have some distinct differences.
People who gain withholding of removal status may live and work in the U.S. However, unlike asylees, people with withholding status cannot apply for legal permanent residence. They also live under a final order of removal (deportation), so if they ever travel outside the U.S., they will not be granted re-entry.
An asylum applicant must show that he or she will face persecution upon returning home, whereas a withholding applicant must only show that future persecution is probable.
Most people apply for asylum and withholding of removal at the same time since withholding does not have a one-year filing deadline like asylum, and it's possible that a judge may decide an applicant is eligible for one status and not the other.