FRA vs Short term interest rate futures

FRA is a forward contract, the long in the contract profits when interest rates rise. Short-Term interest rate futures contract is a futures contract, the long in the contract profits when interest rates fall. Are the above two statements correct?

I don’t think the second one’s correct. Long on BOND futures benefits when interest rates fall.

That is what I thought at first as well. But on CFAI book 6, page 66, under the heading Short-Term Interest Rate Futures Contracts they have: - Treasury Bill Futures - Eurodollar Futures Both have the same pay off formula, and in both cases the long profits when interest rates fall. Is this correct?

Eurodollar futures are meant to look like bond futures. That is, the long profits when interest rates go down. T-Bill futures are decidedly different because there is a deliverable (a T-Bill). A Eurodollar future is not deliverable but is cash settled. Among other things, this gives the T-Bill contract convexity but there is no convexity in the ED futures.