What's the difference between an email service like Yahoo and, say, Thunderbird, which is described as an email client?

Thunderbird like Outlook Express or Outlook for that matter uses your ISP server connection. Hence your mail address will be the address your ISP gave you e.g. @(your)isp.net etc.

Online (web) mail services run on their own servers and have nothing to do with your ISP. Thus the addresses are @yahoo.com or @gmail.com etc.

Is that what you were looking for? Or some other aspect?

I think that's the answer I was looking for, thanks.
I'm considering moving from Yahoo and I wondered what the options were.

Thunderbird would be an alternative to Outlook Express.

Gmail would be an alternative to Yahoo.

etc.

If you want/need a Gmail invitation just ask. I've got a few to share. Just PM me a current address for you.

Invitation?

When I first got Gmail it was by invitation only. This was a long time ago and I don't know if it's changed.

Anyway once you are invited you get a bunch of invitations to pass on. And I have a few left.

http://mail.google.com/mail/help/about.html

Ah.
So, do you recommend them? Just briefly, Yahoo are starting to bug me with their gimmicks. EG: the icon or seal feature at sign in. I applied it to one of my email addresses, but it disappeared within a week or so and I haven't seen it again. The 'keep me booked in for two weeks' feature is kind of a joke too if, like me, you have multiple Yahoo addresses.

I find Gmail to be the best Web based service.

As to Firebird it is Client based (you are the client) as is Outlook Express.

Firebird is to Firefox what Outlook Express is to IE.

For web based: Yahoo; Hotmail; Gmail; etc. I find Gmail to be the best by far IMHO.