Example may help to illuminate the subject:
A - B - C
A-B is 10.10.10.0/24
B-C is 10.10.20.0/23
If 10.10.10.42 wants to do say WOL (Wake-On-Lan) for 10.10.21.42, 10.10.10.42 on subnet A-B can send packet to directed broadcast 10.10.21.255, and B is happy to to forward the packet towards C, so each host in C LAN will receive it, including 10.10.21.42 machine which can then power itself on.
10.10.10.42 couldn't unicast it to 10.10.21.42, because the machine is not on and would not be visible in ARP table, so it would be just dropped after unsuccessful 'ARP WHO HAS' query.
If A tries to send it to 255.255.255.255, B will not forward it to C. 255.255.255.255 is only special case 'limited broadcast' address.
In this example 10.10.20.255 might not be a broadcast at all. So we cannot conclude if address is directed broadcast address without knowing the mask.