how to specify web3 provider/wallet in javascript

Question

If you have multiple wallets installed how do you specify which one to "connect" on following this given example:

function getProviders() {
  if ("solana" in window) {
    const provider = window.solana;
    if (provider.isPhantom) {
      // handle phantom
    }
  }
},

My UI will allow the user to pick from a menu of installed wallets. But the code to connect doesn't seem to specify the provider:

function connect() {
    await window.solana.connect() // <- how to specify wallet
    .then(resp => {
        console.log(resp.publicKey.toString())
    })
    .catch(error => {
        console.log(error)
    })
}

For example, I have phantom and solflare wallets installed. But only Phantom is coming up in window.solana.