They both work completely different ways. Calcium Channel blockers work by blocking a particular pathway inside your blood vessels that lead to a relaxation of the vessel. Calcium is used by these vessels to tighten up their muscles (and in the heart to speed up the rate) and thus increasing blood pressure. Block the calcium and the vessels stay relaxed and the heart rate slows down some.
Beta blockers work by blocking the effect of adrenalin on the blood vessels and heart. Adrenalin tends to tighten up the vessels and speed up the heart, so by blocking it's effect, the pressure is lower and so is the heart rate.
Pharmacists and physicians spend years trying to learn how this stuff works, so you won't get a complete answer here. But this is pretty close.
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