"Psoc is it FPGA or ASIC or both ?" The answer is "Neither" ;-)
PSoCs consist of a CPU (PSoC4 has got an ARM Cortex M0) and a bunch (the amount depends on PSoC family and type) of internal configurable hardware. The connections between the hardware modules are set in the design phase and will be programmed together with all the other settings into the chip. There are some Universal Digital Blocks (UDBs) which can be programmed using a Hardware Definition Language (HDL) named "Warp Verilog" but these aren't FPGA. ASICs usually aren't user programmable as the PSoCs are.
It is pure magic.... amazing engineering with some awesome sauce spread on top.
That being said.. Bob's answer is more technically correct.