Unless you are running your own VPN server, you can be sure that any paid VPN service will log just enough information in order to be able to link your actions back to your IP address.
If they did not, then they would be liable for the traffic for their customers. Imagine if a customer of the paid VPN service, decided to do something highly illegal like downloading or distributing child pornography. The VPN service will have enough bits and pieces logged in order to know which customer generated the illegal traffic.
They literally cannot do otherwise without becoming a safe heaven for crime, or or providing criminals at least a criminals with a 1 time free pass to do something highly illegal. Furthermore it can also be interpreted as allowing someone to mask their own illegal activity by blaming it on the customers who they are not logging the traffic of.
Overall, the VPN services will log information for their own network management needs, but you can bet that it is enough for them to figure out who did what on their network if the government comes knocking.
(They may not all be explicitly recording your session, but there is going to be enough logged to essentially allow them to rebuild the details session if they wanted to)