PA28 pilot reported an NMAC event in the traffic pattern.

Narrative

I was doing the practice ILS XX under the hood into ZZZ. I believe the weather was reporting calm and during our approach my instructor and I had heard traffic saying runway 2 so we continued the approach. At my 10 mile I called low approach only; but after that I didn't say anything about low approaches. I made a 5 and 3 mile call and at the 1 mile I said touch and go since we decided to take the hood off and do a touch and go. That is when we received a traffic alert on our MFD; and we did our touch and go. After the flight; the other plane involved said we were kind of close; but not too close. During our touch and go the other plane on final said they were going to stay at pattern altitude so we turned left at 500MSL and departed; there were no traffic alerts for that. I personally never saw the plane; but the other instructor talked to us about it after the flight. I believe miscommunication was the main cause. If one of us had asked the other about what their intentions were; it could have been avoided.