There was a sine wave input and the output is also a sine wave.

The amplifier can not output a voltage greater than the power supply voltage. The effect is to chop off the peaks and troughs of the signal at just below the power supply voltage. The amplifier below was running on +/- 9 Volts. The input was a sine wave. The output is a sine wave limited at just below 9 volts. MOSFET amplifiers can limit at +/- 7 volts with a 9 volt supply.

When a signal limits (see above), the original signal is still present but there are also harmonics. These are frequencies which are multiples of the original frequency. The plot below was calculated using the Excel (2003) spreadsheet. You can download this and tinker with it. This plot was calculated as follows ...
Y = SIN(X)+SIN(3*X)/3+SIN(5*X)/5+SIN(7*X)/7+SIN(9*X)/9+SIN(11*X)/11
The pattern is easy to spot. The Excel formula can be changed to add or remove harmonics. If sufficient harmonics were added, a perfect square wave would be produced. The pattern below with the eleventh harmonic is already nearly square. A limiting amplifier produces a lot of energy at these higher frequencies. This tends to overload the tweeters in HiFi speaker systems so they fail first when the music is too loud.

Try this formula for a Saw Tooth wave ...
Y = SIN(X)+SIN(2*X)/2+SIN(3*X)/3+SIN(4*X)/4+SIN(5*X)/5+SIN(61*X)/6

Here are some WAV files you can play.