To copy a survey, simply click on [Copy] button after the survey you wanted. A new survey will appear in Edit mode. Save or make modifications to it to get a new URL.
This new survey would be exactly the same as the old one, including theme & logic rules. So remember to make possible changes before you deploy the new survey.
If you need to send a same or similar survey to defferent groups of respondents, you can copy the old survey or simply create different collectors. Be sure to make clear labels so you can identity them later.