Fixed income derivative equivalencies

Having trouble understanding this question from Kaplan study materials.

"Comment 1:

An investor having a long position in a call option on a bond has the same position as if he is long an interest rate floor."

The answer is that this is correct. Why is a call on a bond the same position as a long interest rate floor? I understand that they move in the same direction (if rates drop below the floor/bond prices rise above the strike the positions are in the money), but are they equivalent positions (same exact cash flows), or just directionally the same?


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Interest rates and bond prices move in opposite directions.
s directionally the same.
Not the same exact cash flows, because there is a nonlinear relationship between interest rates and bond prices (convexity for a start).