Do these two sentences imply the same action?
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Not at all!
"Bend your knees, please!" means that the speaker asks the listener to stay in a postition where one or both knees are on the ground. This position is often interpreted as an act of praying and submission (compare Romeo & Juliet).
"Squat down, please!" means that the speaker requests the listener to lower his/her butt to sit like a frog. This position is often interpreted as an act of performing Yoga and Quadriceps Exercises. In some of the Asian countries, there are squat toilets where a squatting down position is needed!
Squatting down generally requires you to have some part of the body which is above the knees when standing erect to be below the knees.
Bending the knees, while this action can include squatting down, only requires the knees to be bent slightly. For example, some people recommend bending the knees to keep the circulation of the blood in the legs unconstricted, but this does not require squatting down.
The first may be addressing someone in a supine or sitting position, the second only someone standing.