What international payment systems do exist?
SWIFT, as a private company, only provide secure transmission of financial messages between the participants. The message types or so vast from customer payments and cheques to financial institution transfers, treasury markets, commodity transactions, Letter of Credits etc. Providing instant, secure, without any disconnection messages together with standardization of these messages are a big job for smooth payments. 
SWIFT does not hold your money, my money nor does it keep an account for the beneficiary bank or remitting bank.
The main underlying money exchange is done through correspondent banking accounts between financial institutions. These accounts are called as nostro and vostro accounts. The debit or credit from and to these account will be confirmed through SWIFT messages. Before SWIFT, the Telex system is used for communication. 

Chinese, CIPS is used only for Renbinmi transactions and is not a competitor to SWIFT. The member banks to this system can use it as a small network but there may be still many banks who are not a member of the system.