And of course, there is the "rail to rail input".
Which means that the opamp's common mode input range goes almost all the way from the negative supply to almost all the way to the positive supply.
Actually, some opamps are optimized to go all the way from a few hundred millivolts BELOW the negative supply, to a few hundred millivolts ABOVE the positive supply. But NOT BOTH conditions simultaneously on THE SAME device.
Read the datasheet. It is your best friend.