There are two major types of IP broadcast addresses; limited. The first broadcast a limited broadcast. The broadcast involves delivering a message from one sender to many recipients. Senders direct an IP broadcast to 255.255.255.255 to indicate all other nodes on the local network (LAN) should pick up that message. This broadcast is 'limited' in that it does not reach every node on the Internet, only nodes on the LAN. BOOTP or DHCP is one of the more popular applications that utilize this type of broadcast. The host sends out a DHCP request to 255.255.255.255. If the DHCP server isn't on the local broadcast domain the router can be configured (using the ip helper-address interface command) to forward to a DHCP server as a unicast packet. Routers by default discard this packet type. One additional note....
"Limited broadcasts MAY be sent and SHOULD be sent instead of directed broadcasts where limited broadcasts will suffice." This is from RFC 1812 (as is most of this info) Requirements for IP Version 4 Routers. So according to the RFC routers should use limited instead of directed if it will suffice.
This brings us to the next broadcast class...DIRECTED broadcast. 192.168.20.255 is a Subnet-directed Broadcast. This is one of the three types of directed broadcast. This is one to every host on the 192.168.20.0/24. This can originate from a host on the subnet or a host not apart of the subnet. If the source is a host not apart of the network the router(s) must be configured to forward ip directed-broadcast. The router connected to that subnet will forward the packet out as a broadcast. Most routers have this function disabled because maliciously abused.
Again my source was RFC 1812 - Requirements for IP Version 4 Routers section 126.96.36.199. You should check it out.