restarting postgresql quickly
If your clients cope well with being disconnected, and don't lose data, you should probably use the first process: Force a checkpoint, then perform an immediate restart. That'll get the server back up and running faster than a fast restart will, at the cost of greater disruption to currently active clients.

Client applications will get errors when they next run an SQL statement. Well written applications will throw away the database connection and retry, so the user won't notice/see anything.

Less well written applications will report an error to the user.

Truly badly written applications will silently lose data (if they swallow exceptions) or perform only part of an operation (if it isn't properly using transactions). These clients will also have problems under other circumstances, and must be fixed.