**EDIT: Oops, I just realized this is in the Routing forum not the SRX forum. The info here is applicable to the SRX prodcuts, I honestly don't know how it relates to the routing platforms.
For starters, "request system power-off" is only available, I believe, on SRX240 and lower. The SRX650 does not support power-off, and I don't think the 3k or 5k do either.
When you halt the system, it shuts down the OS and gracefully terminates processes, syncs disks, etc. It's a holdover term from the Unix roots that Junos is based on. Halting won't turn the device off per se, it's still "on", but the OS isn't running so it doesn't do anything. Once a system is safely halted, you can remove power.
"request system power-off" on the SRX240 and below will halt, and then actually turn power off. I'm not real sure why the 650 and up don't support the full power down, but I suspect it has something to do with the more modular architecture of those devices vs. the mostly monolithic architecture of the 240 and below.