As 127.0.0.1 is known as the loopback address, is there a shorter term to refer to 0.0.0.0 other than "the IP address who means all IP address on local machine"?
Sometimes it is called "wildcard address",
INADDR_ANY, or "unspecified address". The official name is "source address for this host on this network" (RFC 5735, Section 3). It must not appear in packets sent to the network under normal circumstances:
This host on this network. MUST NOT be sent, except as a source address as part of an initialization procedure by which the host learns its own IP address.
But if it appears as destination address in incoming packet it should be treated as broadcast address 255.255.255.255 (RFC 1122, Section 3.3.6)
0.0.0.0/0, which covers every IP on the Internet, is different from
0.0.0.0/32 or just
0.0.0.0, which is what the OP seemed to be asking about.
INADDR_ANY, which is primarily used when accept(2)ing to allow incoming connections regardless of the destination IP address, while
0.0.0.0/0 is "all addresses" (most commonly used in routing when specifying a default gateway, and in firewalls when specifying default rules), and
0.0.0.0/32 is "the unspecified address" (used most commonly in application-level programming to say, "this address is wrong/uninitialized").