PRI and SIP Trunking are protocols that connect your business phone system to the PSTN (Public Switched Telephone Network). Usually PRI and SIP Trunking require a hardware device in your office called a PBX. Most PBXs can support both PRI and SIP Trunking connections, either directly or with a special adapter.
A PRI is a single line with 23 voice channels and one data control channel (T1), that allows your business to hold 23 calls simultaneously. This is not the same as the number of phone numbers a business has. Your business may have 50 phone numbers that are directed across a single PRI, however, you can only have 23 phone conversations at once.
SIP Trunking sends your voice connection over an existing data line, and is commonly known as VoIP. Your call goes over the SIP Trunk and is treated like every other piece of data on that connection - webpages, email, etc.
The major differences:
PRI is a physical connection to the PSTN over a dedicated line that only serves voice transmission.
PRI uses a circuit switched model for making voice connections between people.
PRI has a guaranteed Quality of Service (QoS)
SIP Trunking is a virtual connection to the PSTN over a physical line that is often shared over your existing data connection.
SIP Trunking uses a packet switched model for making voice connections between people.
SIP Trunking is typically best effort.
Read more about PRI and SIP on the One Voice website.