An APC is an armored taxi. Its purpose is to transport its primary weapon ( the 8-12 soft squishy things in the back) to a point near the target in relative safety, then dump them out to achieve their objective. Armor is thick enough to protect against small arms fire and shell splinters, armament is the minimum necessary to give some fire support to the dismounted troops - usually just a machine gun or two.
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The IFV is more heavily armed and armored. It is intended to if necessary proceed all the way on to the objective and even fight with the infantry still mounted. It has more firepower able to deal with a greater array of targets up to and including tanks in some cases and typically offers greater protection to its occupants from a wider variety of enemy weapons.
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World War 2 half-tracks such as the American M2 and M3 series and the German Sdkfz.250 and .251 were early armored personel carriers. They were issued to infantry battalions in armored (tank) divisions to allow the infantry to have similar mobility to the tanks they were operating with while at the same time offering them some protection against enemy fire. The half-track was a clearly inferior way to achieve this and was replaced quickly after WW2 by fully-tracked APC's.