I would have thought the same thing. Though I didn't use /etc/init.d/postfix start|stop|restart . I just used $postfix reload. Must not be the same.
Oh yeah, that does something different. Probably reloading the configs?
"postfix reload" tells the master process 1) to reread its config,
2)tell the running processes to exit (at their leisure, so that what they're doing gets finished)
3) start new versions as they're needed, with the new configurations
The master process continues to run. There should be no interruption of service.
Stop stops all processes. Start starts them. There's a period of time (short, usually, but on a busy server it can be a fairly long time) between when processes start shutting down and when they finish. There's another interval while the master starts up. So there's an interruption of service.
There are a very small handful of things that the difference matters to. Upgrading the binaries is the obvious one, but changing the addresses (inet_interfaces and inet_protocols) that postfix is listening to is one of them. (The only others I can think of are changing the queue_directory and daemon_directory, but I don't think anyone does that often.... There might be a handful of others. The log file should tell you about them. )