Ok, thank you both, and sorry for the delayed response. I now know a little more than I did before. But there are some things that still do not make sense to me.
I was already aware that ETH functioned differently to BTC in that ETH allowed people to engage in smart contracts.
However I thought it was also possible for ETH to function like BTC and be used for normal transactions.
I was
not intending or trying to enter a smart contract or an ICO purchase. I was simply trying to send ETH from my Bitstamp exchange wallet to my CEX.IO wallet. I don't understand why an exchange like Bitstamp wouldn't allow users to do that, and I don't understand why an exchange like Bitstamp would even be bothering with smart contracts.
I do not get any warnings about trying to withdraw BTC, LTC or BCH. So why do I get this warning when I am about to withdraw ETH? And can I not just send ETH to another exchange - do I really have to go through my private wallet first?
You can send ETH to the address you want. Just don't send them from the exchange to an ICO or smart contract.
Well, I have now given that a try. I only sent a small amount of ETH (an amount I could afford to lose) from my Bitstamp address to my CEX.IO address, and now they've been lost. It seems Bitstamp forced me to send the ETH as if I were entering into a smart contract, and the CEX.IO address didn't like it. I see from searching online that other people have had exactly the same problem (and with the same exchanges).
Can anyone explain why Bitstamp would force people to send ETH as if they were entering into a smart contract? And are there any other coins where this sort of thing can happen? (E.g., is it easy enough to send Dash or Monero from one exchange to another, or do you have to be careful there too?)