what is the difference/similarity between MIPS and FLOPS?

Study them using google and you will find out a lot from using the full forms,

MIPS=millions of instructions per second

FLOPS= floating point operations per second

mips talks about instructions which could be any type of instruction.

flops talks about a specific type of operation present in the instruction which is related to decimal numbers.

so they are not related in measuring as both use different reference points.

MIPS and FLOPS ARE metrices for calculating processor speed.

"MIPS=millions of instructions per second FLOPS= floating point operations per second"

Computer architectures have been made to "cut corners" to make them more efficient. This causes different architectures to have different run times for identical programs (a set of instructions). This makes a comparison using MIPS (relatively) meaningless over different architectures, but great to show performance upgrades in the same (or similar) ones.

FLOPS measure for a precise type of instruction. Therefore, it can be used to see which architectures are best for specific types of programs.

If, however, there wasn't a specific task in mind. MIPS could be used to find a computer architecture that is a Jack of all trades.

The intent of the comparison matters here.

So they are related only in the fact that they are metrics for calculating processor speeds. They are independent on how they operate or what they are used for.