When you conduct a survey you're typically asking questions, whereas when you're performing or answering a survey, you're responding to questions that are presented to you in said survey. I hope that's what you were trying to understand, let me know if you're still unsure :)

To my understanding, they mean the same thing, but "conduct" is a much more common way to say it. I would not use "perform" to mean responding to the survey questions. I have never heard someone say that. People say "I took a survey" (like "I took a test"), or "I completed a survey", or "I filled out a survey" (like "I filled out paperwork").