In general, HARQ is a physical layer protocol, which combines the use of forward error correction (fast, because it does not involve any retransmission) with retransmission request, when the errors are too severe for FEC to correct them. This is at the physical layer, as bits encoded in symbols flow over the wireless interface.
ARQ works above that layer, to detect and correct any errors in the data packets. In principle, the physical layer errors can all be corrected, but there could still be parity check errors or packets out of sequence, above the physical layer. For instance, the errors can occur before the data packets were converted into that physical layer stream of symbols, in the RF transmission end.
So, the idea is that most errors in wireless will occur in the RF link, and that therefore, most errors will be corrected by fast techniques like FEC, which are part of HARQ. But that's not the ultimate check, as other data packet errors might also have occurred along the way.
Even wired protocols work that way, really. Ethernet frames have their own 32-bit CRC, which is independent of any IP or other parity check, above the MAC layer. Ethernet does not itself do any retransmission requests, but the idea is the same. WiFi does do retransmission requests, at layer 2, for the same reason as LTE. The RF link is more subject to errors, than would be a wired Ethernet link.