The EVM is a virtual machine, meaning it doesn't matter if you are connecting via a public one, a paid one, or your own RPC, you will interact with it in the same environment. This concept is called a holographic computer

You interact with the EVM, this is where all the "programs" (smart contracts) are "hosted" (deployed and stored). You connect via a RPC but the EVM is the same for everyone on the same chain, for example Ethereum