What PlayStaion 2 model is it?

I had a PlayStaion 2 (PS2). It looked like the original PS2, but the PS2 had more options that the ORIGINAL PS2, for example, the DVD player function, for the options during playback, there were more options. Also another key feature, the PS2 had a built-in sensor. I bought a PS2 remote that came with a sensor to plug into the controller slot, I needed that for one of my PS2s or else the remote would not work. However, for this model of PS2, it had a built in sensor, so with nothing plugged into the controller slot, I could point the remote at the PS2 and control it such as for DVDs. My question is, what is/are the model number(s) for that type of PS2 with those newer features. Remember, it looked like the original PS2. Please name your source(s) if possible, Thank you very much for your help!