Which is the difference?
The GND is the ground of the batterie (3.7V)and should be connected to all GND?
the GND1 is the ground of the output (5V) and should be connected to all GND1 AND NOT to the GND?
If GND and GND1 has to be connected, is true that it have to be connected with a very small wire?
You can connect them together in this application. They should, for proper operation and stability, be connected at the same point. What I mean by this is, connect all the GND together, then connect all the GND1 together, then connect the common GND to the common GND1. Where you connect the two grounds together should be a close to pin 4 (GND) of the regulator as possible. That should not be hard with this type of chip package. TI give some good recommendations for layout in their datasheet. http://www.ti.com/lit/ds/symlink/tps61200.pdf