If you import the seed phrase to the Electrum wallet on your new computer,  you will see your coins there too. If you are having internet connection and both wallet synchronized with the blockchain, definitely the both wallets are the same, if you spend coin on one, it would appear on the other. But having two online wallets for the same purpose to track and spend the same UTXOs, being online wallets makes it more prone to attack, I will advice you to delete the wallet from the old laptop after you import your seed phrase on the new wallet.