I was thinking of renting a car for a trip. We have working cars, but my wife has insisted that we rent a car when driving to Southern California.
As for charging for energy - it depends, but usually yes. All of them communicate with the charging provider and you're supposed to have some sort of account (with a credit card on file) in order to use it. And there are several systems and each one will need an account.
Tesla had the great benefit when they initially came out with their charging stations. Charging is free if the Tesla vehicle was purchased before a certain date. They said it wasn't sustainable and may have encouraged wasteful use of resources. They also brought it back when some vehicles weren't selling. If a Tesla was sold with free charging included, it's included for life. Some might also buy a used vehicle that came with free charging when sold new, as the free charging plan transfers to the new owner.
https://electrek.co/2020/05/27/tesla-removes-free-supercharging-model-s-x/
Their charging stations aren't compatible with any other vehicles. I test drove a Tesla once, and the Tesla employee (they're not sales specifically) showed us the adapters they provide to use with other charging systems. Not sure what the price is now. They also have different charging speeds. I believe it's up to two charging connectors per station, and having both connected might slow it down with some of their setups. Also Tesla may charge by the kWh, but some of their systems charge by time connected.
I think it gets really complicated with Tesla. They have variable rates and not all their chargers are high speed Superchargers. I heard something about a limited amount of free charging if someone is on a trip away from home. Even if charging is free, I believe they will start charging money if it's connected and stopped charging for a certain period of time. They want the customer to remove it and move so that another vehicle can charge. This is similar with other charging systems.
I've heard of a few places that have maybe one or two hours of free charging subsidized by the host. An example would be some ChargePoint charging stations at Target parking lots where they provide two hours of free charging. I looked up one I've seen before (Fremont, CA Target store) with ChargePoint Level 2 chargers at 5 kW. After that it's $2 per hour. At that charging rate, a Nissan Leaf with a 40 kWh battery should take about 8 hours to fully charge, although most people will be traveling short distances and topping off. There are also faster chargers.
Hope I didn't bore you with all the useless information. It's actually quite complicated. However, Tesla has a great infrastructure with its charging stations - especially that they're faster than most other commercial charging setups.