If you’ve currently submitted your application for the Permesso di Soggiorno at the Post Office or at a Patro Nato in Milan, your appointment may be in three to six months from the day you’ve applied, or less – if you are very lucky. Hence you have only your permesso di soggiorno receipt as proof of your application.
According to the Portale Immigrazione website, “those who have a residence permit being renewed can only travel between Italy and their country of origin, however showing the receipt of application along with the valid passport at the border“.
If only your Visa is still valid can you visit other Schengen areas. If you need to travel to another country other than your home and within the Schengen Area, then you must request the Permesso di Soggiorno Provvisorio. Read how to apply for the Permesso di Soggiorno Provvisorio here.
So the answer is, you can travel to your home country with your ricevuta but you cannot travel to other Schengen Areas with a permesso di soggiorno receipt. I have seen some people advise you can without being caught, but that’s a dangerous risk I wouldn’t advise anyone to take.
Read my post on How to Apply for the Permesso di Soggiorno Provvisorio here and also learn why you shouldn’t travel with just your Permesso di Soggiorno Receipt.