mjhjmtu

I was wondering what is the role of this special-use address.

The similar 0.0.0.0/8 represents a host with no IP assigned,but it's not the same with the 0.0.0.0/32 address

What is the difference?

According to the IANA which is the authoritative source regarding IP address assignment. 0.0.0.0/8 is reserved:

From the IANA IPv4 Address Space Registry page:

Prefix Designation Date WHOIS RDAP Status [1] Note 
000/8 IANA - Local Identification 1981-09 RESERVED [2]

And the footnote [2]:

0.0.0.0/8 reserved for self-identification [RFC1122], section 3.2.1.3. Reserved by protocol. For authoritative registration, see [IANA
registry iana-ipv4-special-registry].

RFC1122 states that:

3.2.1 Internet Protocol -- IP

 3.2.1.3 Addressing: RFC-791 Section 3.2

 We now summarize the important special cases for Class A, B,
 and C IP addresses, using the following notation for an IP
 address:

 <Network-number>, <Host-number> 

 or
 <Network-number>, <Subnet-number>, <Host-number> 

(a) 0, 0

 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.

 See also Section 3.3.6 for a non-standard use of 0,0.

(Section 3.3.6 is related to all zero broadcast addresses)

Conclusion

0.0.0.0/8 is the first /8 network of the Internet and it is reserved.

0.0.0.0/32 is the very first host address of the Internet, and, as part of the 0.0.0.0/8 network it is reserved.

A 0.0.0.0 address is only use locally as part of an initialization procedure, I.E. DHCP / BOOTP.
This procedure being local, it doesn't involve a subnet mask, so there's no notion of /32.

I think you are confusing networks with addresses because packets have source and destination addresses, but no mask information. That means that any host address is the full 32 bits of the address.

An address in the 0.0.0.0/8 network can be used as a source address when a host does not know its own address, e,g, in a DHCP request, but they can never be used as a destination address because a host cannot be assigned an address in that network.

This is spelled out in RFC 1122, Requirements for Internet Hosts -- Communication Layers:

(a) 0, 0 

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.

See also Section 3.3.6 for a non-standard use of 0,0.

(b) 0, <Host-number> 

Specified host on this network. It MUST NOT be sent, except as a
source address as part of an initialization procedure by which the
host learns its full IP address.

Network masks (or a mask length, such as /8) are used in routing tables by a router to determine where to send packets destined for a particular address. A destination address is masked to see if it matches any routing table entry, and if it does not match any routing table entry, the packet is dropped. Every IPv4 address is in the 0.0.0.0/0 network, so every address would match that network in a routing table, which is why it is used as a default route. Routers drop any traffic for which they do not have a route, but because 0.0.0.0/0 matches every address, then a router with that network in its routing table has a match for every address.