Will there be two different input producing the same hash result? (hypothetically, a 200-bit input entropy produces the same hash result of 20000bit...)
If you are generating private keys by using SHA256 on different inputs, then yes. Indeed, there will be
many more than two inputs which will result in the same output.
For SHA256, you must append to the end of your input the length of that input expressed as a 64 bit number. This places an upper bound on the length of the input, which will be 2
64 - 1 bits. For reference, this means that any data up to approximately 2 exabytes (2 million terabytes) in size could be used as in input to SHA256, if you had the hardware capable of processing it. Given this, and given that we know that SHA256 will always produce a 256 bit output, then it is easy to see that there will be many billions of inputs which must map to the same output.