If you have ever switched your wallet from Ethereum to Base and noticed the address bar did not change at all, that was not a glitch. For most wallets, on most networks, your address really is identical everywhere. Understanding why helps explain what a wallet actually is, and it also helps you avoid a specific, easy to make mistake involving networks where the address is not the same.
An address is math, not a database entry
A wallet address is not something a network hands out or stores in a lookup table somewhere. It is calculated. Your wallet holds a private key, a large random number, and from that key it derives a public key using elliptic curve math. The address itself comes from hashing that public key with the Keccak-256 function and keeping the last 20 bytes of the result.
None of those steps involve asking a network for anything. The calculation only needs your private key and a fixed, standardized formula. Base, Ethereum, and any other network that uses the same curve (secp256k1) and the same hashing scheme will always compute the same address from the same key, because they are running the identical formula on the identical input.
This is why the term "EVM compatible" matters here. Base, Ethereum, Arbitrum, Optimism, Polygon's PoS chain, and a long list of other networks all implement the Ethereum Virtual Machine and its account model, including this address derivation method. Your wallet is not really creating a separate "Base account" and a separate "Ethereum account." It generates one address from your key, and every EVM compatible network you point that wallet at recognizes the same address, because they all agreed on the same math from the start.
What actually differs between networks
If the address is identical, what changes when you switch from Ethereum to Base in your wallet? The state behind that address does. Each network keeps its own independent ledger of balances, contract deployments, and transaction history. Your address can hold ETH on Base and hold nothing at all on Ethereum, or the reverse, because "how much ETH does this address have" is a question with a separate answer on every chain. The address is a shared identity; the balance is local to each network.
The other piece that changes per network is the chain ID, a number baked into every transaction before it gets signed, as described in more detail in what a chain ID is and why it matters. The chain ID is what stops a transaction you approved on Base from also being valid on Ethereum, even though the address sending it looks identical on both. Address derivation and transaction validity are handled by two completely separate mechanisms, which is part of why this system works as smoothly as it does.
Where this stops being true
The same address trick only works between networks that share the same underlying address format and signing scheme. It does not extend to every blockchain you might have heard of.
Solana, Bitcoin, and most Cosmos based chains use different cryptographic curves, different hashing methods, or different address encodings entirely. A Solana address is a base58 encoded Ed25519 public key. A Bitcoin address is built from a different hash and encoding scheme. There is no shared formula linking a Base address to a Solana address, so your Base wallet address will never appear as a valid destination on Solana, and a Solana wallet cannot generate your Base address either.
This is the source of a real and costly mistake: sending an EVM asset to what looks like a matching address on a non-EVM chain, or pasting an address from the wrong network into a withdrawal field. If a network is not EVM compatible, treat its addresses as belonging to a completely different system, not a variant of the one you already have. When in doubt, send a small test amount first, and double check the network selector in whatever app you are using before confirming a transfer. For the related case of sending the right asset to the right address but on the wrong EVM network, see what happens if you send tokens to the wrong network.
It is also worth separating this from a different topic: why the same token can have different contract addresses on different chains, covered in why the same token has different addresses on different chains. That is about smart contracts, which are deployed separately on each network and get their own addresses based on how and when they were deployed. Your personal wallet address, tied to a private key you control, works by a completely different and much simpler rule.
Why this is worth knowing
None of this requires action on your part. Your wallet handles the derivation automatically, and Simple Base Swap, like most EVM wallets, will show you the same address regardless of which EVM network you are viewing. But knowing why makes a few things easier to reason about: why adding a new EVM network to your wallet never asks you to create a new address, why your recovery phrase backs up access to every EVM network at once rather than one at a time, and why that same convenience does not extend to fundamentally different blockchains that were never built to share the formula in the first place.
Sources: Ethereum Yellow Paper, account address derivation, EIP-155 chain ID specification, Base network documentation.