It sounds like you have on Sharing with another Galaxy user feature on so it let you know when u have called or text them
Not sure because I dont use that feature but the donut in screenshot indicates Samsung customizable service with another Samsung or Android I believe what they called it back thenCould it also be part of the Call and Text on Other Devices feature from Samsung? So in other words, the phone icon means the other person is texting from their phone, but if they used a tablet or a PC, it would show the corresponding icon?