For optimum performance they should be the same diameter, regardless of the rim size. For example 195 50 15 tyres have the same diameter as a 175 70 13 tyre. Though they differ in size, they make up for it in tyre height and width.
In your case, they will most deffintely be a different diameter. There are multiple issues with that, check for brake caliper clearance inside the rim, and for rubbing in the wheel arch lining. It will offset the speedo reading, and different rim size and weight can also put unnecessary stress on the steering rack.
Here is a link to a useful tool to compare what you need and help you understand tyre and rim fitment: