I guess it doesn't matter whether it's typed in to the computer or on the device itself.
Technically, if you were ever to enter your seed on the same computer, which you shouldn't really do, it could be a threat.
But the inconsistencies with electrum using different addresses than what's on the trezor website is a little weird.
By default, Electrum generates native SegWit addresses (bc1...) while Trezor Wallet supports only legacy (1...) and nested SegWit (3...) addresses. The upcoming Trezor Suite (a desktop and mobile app) will introduce an official support for generating native SegWit addresses. However, it is still in early beta. If you want to use the same type of addresses as Trezor Wallet supports then you should take a closer look at the following screen which appears when adding a new wallet using a hardware device.
First, you have to select what type of address you want (p2sh-segwit would be the best choice if you need to be able to access your coins through Trezor Wallet for some reason). Then, you can modify the derivation path. The last number is the number of the account you want to access. Zero is the first account, one is the second and so on.
To rectify that I guess we should say, is that just entering the addresses given to me by trezor manually into electrum as a watch wallet?
If you enter your address manually into Electrum then you will get a watch-only wallet. However, in order to be able to spend coins using your hardware wallet, you have to choose another option ('Standard wallet -> Use a hardware device').
But then if you go to send from that, the secret key, is still stored on the device and never transferred to electrum?
Yes, your private keys never leave your device. Electrum only knows your Master Public Key from which new addresses are derived. If you disconnect your hardware wallet, Electrum will act as a watch-only wallet.
But then what if it's a wallet with a passphrase I set on electrum but want to see that address on the trezor site. Same thing by just entering the pass. I guess think of it as a backwards compatibility type question.
I hope that you don't confuse a passphrase with a password encrypting Electrum wallet file. Once you enable passphrase support in the settings on Trezor Wallet, both Electrum and Trezor Wallet will prompt you to enter your passphrase every time you open your wallet. You should see the same addresses on both wallets using the same passphrase.