In my opinion: soft reset: boots from the reset vector. hard reset: pull the electrical level of the cpu.
This can very from chip to chip I assume. The hard reset is probably agreed to be the reset line on the device (pin, ball, etc) when pulled in a certain direction puts some or all of the chip in reset. Soft reset, could be as simple as a branch to zero or branch to the reset vector, or it could be a register you write or a bit in a register that causes a hard reset, or perhaps something close to a hard reset, imagine a layer inside the chip, the hard reset hits the outer layer, the soft reset hits some inside layer possibly not the whole chip. for example you maybe you dont want to fall off the pcie bus so you leave that alone. Normally jtag (or some portion of it) for example shouldnt be touched by either reset. When software pulls a reset line it kills itself, who is going to release that reset? Something in hardware, many ways to solve this, but if solved with something that has a digital component to it that digital section shouldnt get hit with the reset the software has hit or you again get stuck not being able to release it.