The broadcast address is a real, reachable address
Every subnet reserves its highest address as the broadcast address — a packet sent to it is delivered to every host in that subnet simultaneously, rather than to one specific device. For 192.168.1.0/24, the broadcast address is 192.168.1.255; for the smaller 192.168.1.0/26 subnet, it's 192.168.1.63. Because it's reserved for this all-hosts purpose, it can never be assigned to an individual device — assigning it would create a conflict every time something tried to broadcast to the subnet.
The wildcard mask is not an address — it's an inverted mask
The wildcard mask is the bitwise inverse (NOT) of the subnet mask: wherever the subnet mask has a 1, the wildcard mask has a 0, and vice versa. For a /24 network, the subnet mask 255.255.255.0 inverts to the wildcard mask 0.0.0.255. For a /26 network, the subnet mask 255.255.255.192 inverts to 0.0.0.63. It isn't an address anyone connects to — it's a bit-pattern used as an input to certain configuration syntaxes, most commonly Cisco access control lists (ACLs) and OSPF routing configuration, both of which use wildcard masks instead of subnet masks by convention.
Why wildcard masks look "backwards" to people used to subnet masks
With a subnet mask, a 1 bit means "this bit must match exactly" and a 0 bit means "this bit can be anything" — but with a wildcard mask, the meaning of 1 and 0 flips: a 0 bit means "this bit must match" and a 1 bit means "this bit can be anything." This inversion is precisely why the two masks are bitwise opposites of each other for the same subnet — they encode the identical match/don't-care pattern, just with the bit values reversed.
Where each one shows up in practice
The broadcast address matters whenever a protocol needs to reach every host on a segment without addressing them individually (e.g. DHCP discovery, ARP requests on IPv4 networks). The wildcard mask shows up specifically in router and firewall configuration syntax that predates or deliberately avoids CIDR notation — if you're writing a Cisco ACL rule or an OSPF network statement, you'll be asked for a wildcard mask, not a subnet mask, even though both describe the exact same address range.
A quick way to keep them straight
Broadcast address = a specific reserved IP at the top of the subnet's range, used to reach all hosts. Wildcard mask = the inverse of the subnet mask, used in specific configuration syntaxes to describe a match pattern rather than a real address. If a value looks like a normal IP address and is described as something you send a packet "to," it's the broadcast address; if it's described as a mask used inside a configuration rule, it's the wildcard mask.