These terms get used interchangeably, but they're genuinely different projects with very different costs and reasons to undertake them.
New visuals, new layout, often on the same platform and content management system — faster and cheaper than starting over.
New platform, new underlying structure, often new content — justified when the existing platform is genuinely limiting functionality you need.
Quoting for a rebuild when a redesign would solve the actual problem means paying significantly more than necessary, for a project that takes far longer.
If specific, nameable content or design issues are the problem, a redesign usually suffices. If the platform itself can't support what you need, a rebuild becomes the genuine answer.
Find out honestly which one you actually need.
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