A little 8" speaker is an ordinary woofer, not a sub-woofer. That is why you turn up its volume control too high.
If it is half-decent or better then it will have a flat response down to about 60Hz.
A half-decent or better sub-woofer has a flat response down to 20Hz or lower so you can feel the vibrations.
A volume control is never made to provide full power when it is turned to max. It allows you to turn up the volume much higher for sounds that are played softly. If the volume control is turned up to max rotation then with normal music the amplifier will be clipping like mad.
A volume control is not linear, it is logarithmic. So when it is turned down to half-rotation then the power is 1/10th as much as when it is turned to max. 1/10th the power sounds half as loud. 10 times the power sounds twice as loud. That is why volume controls are logarithmic.