What is the difference between seed phrase and private key?

[o_e_l_e_o]

Like Electrum seed phrase, Iancoleman can not be used to generate Electrum wallet private key from its seed phrase because the way the seed phrase is generated on Electrum is not the same as it is generated on BIP39 wallets.

Electrum seed phrases are generated very differently than BIP39 seed phrases, as you say, but this is not why you cannot import them to Ian Coleman's tool. The reason they do not work in Ian Coleman's tool is because the process of turning the seed phrase in to a master private key is (very slightly) different. Ian Coleman's tool doesn't care how the seed phrase was generated, only how it is used. Essentially the only difference is in the salt for PBKDF2 - both concatenate your passphrase (if you are using one) with another word, but BIP39 uses the word "mnemonic" whereas Electrum uses the word "electrum". If you make that very minor change in the code for Ian Coleman, plus an additional change to have to stop checking for the BIP39 checksum (which does not exist in Electrum seed phrases), you will be able to recover your Electrum addresses.

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I would also suggest doing this in this specific case, but do it with a hardware wallet paired with Electrum rather than an Electrum software wallet.

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[Darker45]

The private key is a very long letter/number.  But do most people write that down as well?

Nope, if you have the seed phrase there is no more need to keep a copy of your private key. Your private key, after all, is derived from your seed phrase. Having the seed phrase under your sole control means you also have the sole control of your private key. If in the event that you specifically need your private key for whatever reason, you could always extract it from your seed phrase using iancoleman's BIP39 tool.

What if you only have the private key but not the seed phrase?

What specifically about it? Take note that your seed phrase could give you your private key but not the other way around. I mean, you cannot derive your seed phrase from your private key.

So if what you have is a private key, you could import it to a wallet and be able to take control of your funds, but only those that are in the address whose private key you are in possession of. Generally, 1 address = 1 private key, but 1 seed phrase = unlimited private keys. So if you have a wallet and lost the seed phrase but have the private key of one of the addresses, you couldn't possibly retrieve those funds that are deposited in addresses other than the one of which you have the private key. 

[JoyMarsha]

The private key is a very long letter/number.  But do most people write that down as well?

I don't think so. The only time I have made use of my private key is when am importing my wallet address to MetaMask. What I did was just copy my private keys from my trust wallet, to paste them on MetaMask. Apart from that, I wouldn't have made use of my private keys. Private keys are not something to write down on a piece of paper. The number is very long