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logic gate is nothing but the components which logically performs on inputted signals.
eg: AND, OR, ,XOR, etc...
logic cell is nothing but, the actual internal circuitry, which performs the logical operations inside the logical gate.
eg: mos level construction of NOR, NAND gate.
Logic cells consists of LUTs and their associated logic.. such as mux, and/xor gates... they make up an LC in FPGA terminology. Xilinx uses Logic Cells to describle its FPGAs where as Altera uses Logic elements.. functionally both are the same, though the architecture may be slightly different. In FPGA, the basic building block is an LC/LE. FPGA area is calculated based on the number of logic cells/logic elements/slices..
logic gates are the basic building blocks of modern digital design. The most important ones being NOT, NAND and NOR. You can construct any logic using these gates and also construct any other logic gate using these basic ones.
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