The difference between Asylum and Refuge status is that Asylee submits application in the US and Refugee apply outside the US.They are the same thing in the rest of respects.
There are basically four grounds: race, religion, nationality, membership in a particular social group or political opinion. Ever since ratification of 1999 United Nations Convention Against Torture, convention against torture claimed can be raised along with above-mentioned basis. However, CAT requires higher level of possiblity. It's been indicated by so many case laws that while the four grounds may require 10% possibility of persecution, CAT applicant needs to prove 90% possiblity of persecution.
The application of asylum is first reviewed by asylum officer. In cases asylum officer can't decide the eligibility, he will refer the case to an immigration judge. At both stages,I strongly recommend assistance of counsel because asylum procedure comes up with evidence presentation, cross-examination, argument with INS attorney , a lay person can't handle all of these.
Finally, I need to warn those people who are out of status and wish to apply for asylum that you will somehow take risk by submitting asylum application because you will be subject to removal if your case are finally denied by immigration judge. Of course, you can appeal, keep fighting in the court, it could be very time-consuming and you may suffer a big loss in your bank account.