Sort of, but this is actually just that no device signature at all is being read, rather than a situation where it's reading a legitimate signature from the chip, but just not the expected one (e.g., ATmega168 vs ATmega328P).
I know you said you checked your connections, but I recommend you to triple-check the wiring is like so:
Note especially that pin 10 on the programmer board is connected to the RESET pin on the target board.
If the connections are right, you might have a defective jumper wire. The internal electrical connections can sometimes break or become intermittent. you can check the continuity on each wire with a multimeter or LED or try swapping out the jumpers for different ones.
And then there is the elephant in the room that most people use "Burn Bootloader" as an attempt to resuscitate an Arduino board that has mysteriously stopped working. That does sometimes recover the board, but in the case of physical damage, no amount of "Burn Bootloader" can ever put the magic smoke back in the chip.