I do not think that they are completely synonymous. The Oxford dictionairy defines them as quoted below:
survey:
1 a general view, examination, or description. 2 an investigation of the opinions or experience of a group of people, based on a series of questions. 3 an act of surveying. 4 a map or report obtained by surveying.
Questionnaire:
noun a set of printed questions, usually with a choice of answers, devised for a survey or statistical study.