Compressive strength is the maximum compressive stress that under gradually applied load a given solid material will sustain without fracture. The term most commonly used for knowing the strength of solid materials, whereas firmness is generally used with non solid biological materials like fruits or other tissues. While measuring firmness we actually measure the force per unit area which is able to cause penetration of a given plunger of specific diameter. Both are different the first one is the measure of threshold load capable of causing deformity whereas the second one is the measure of load which has caused deformity.

there is positive co-relationship between these two parameters in case of developing fruits adavancing towards fruit maturity.

I confirm the answer of Dr Shashi Kumar

The answer given by Dr. Shashi Kumar is perfect.