problem is that user's service units are run by systemd's user session, that it is created when user logs in and removed when user logs out, stopping all user units. But my raspberrypi is running as a home server, so no user is logged in usually. I want synching on raspberry running all the time. So I need to run it from a system unit instead of a user one.
So when it is setup as

pi@rpi$ systemctl --user enable synching.service

that is my pi user enabling the syncthing user's service for himself.
That's what you want on a desktop or a laptop: when you log into you desktop, synchting is started automatically.

when instead is setup like this

pi@rpi$ sudo systemctl enable syncthing@pi.service

this is root (via sudo) setting a service unit for syncthing, using a template unit file: the part you set after the @ when you enable the service is passed as argument, which in unit file is used as a "variable" called %i:

This is part of the unit file on disk, called syncthing@.service:

[...]
[Service]
User=%i
ExecStart=/usr/bin/syncthing serve --no-browser --no-restart --logflags=0
Restart=on-failure
[...]

There the argument set the user which will be used to run the service.

Systemd will run syncthing at boot (after network is set up) as my user pi, whitout the need of an entire user session for it.

I hope all of this make some sense :P