Confusion with input type of ADCs in datasheets
Is the above category about the source types(unipolar or bipolar), or
  is it about type of the amplifier itself?


You are confusing input types with power supply types. An ADC can have either single-ended or differential inputs. Its power supply can be unipolar (ground with a single + power feed), or bipolar supply with something like +/- 5 volts.


In terms of compatibility (ideally) you want the power source for the ADC to match the signal power source, unipolar or bipolar. This way a unipolar ADC is not likely to get a input voltage more negative than ground. If so then the input has to be scaled or clamped so it does not go negative. Most MPU's have unipolar ADC inputs so some method is needed to insure the ADC only sees voltages within its range of operation. It can have differential inputs but with a single-ended source the (-) input is connected to signal ground or the (-) output of a differential source.
Bipolar ADC's are normally standalone types with 12 to 24 bit resolution and may or may not have differential inputs. But the ADC input voltage can go negative close to the negative supply rail. It may have a parallel or SPI port to communicate with a MPU. The cost are higher and much more detail to digital noise isolation is mandatory for these ADC's, which may have very high sample rates.
Due to their lower cost most ADC's have unipolar power supplies as low as 3.3 volts, with a range of 0 to 3.3 volts. If in a MPU it normally had 10 bits of resolution, but some offer 12 bits of resolution with a single pair of differential inputs. As long as the source stays within the ADC's specified range then there are no damage or ADC reading error issues.
In some cases manufactures specify a maximum series resistor value to limit current if a over or under voltage condition could happen, usually 1 K to 10 K maximum to avoid errors due to the internal sample/hold capacitor needing a minimum source impedance to charge up quickly during sample time.
These resistors can be used with low-leakage diodes (not Zener or TVS diodes) to the power/ground rails or dedicated voltage clamps to limit the amount of over/under voltage possible.