Outlook express {OE} & Thunderbird {Tbird} are called "pop" mail clients

short version is
they access your Verizon email account and get your messages that way - so when you open OE or Tbird it will either, depending on your set up it, go get the messages or may wait until you click the get messages button
- mine is set to get them on opening with my password.

that's why you have to put in the account & passwords info when you set them up.
If you get tbird you can also import all your OE stuff during setup, just like Firefox did with IE settings.

then you would set Tbird as your default email - you can still keep OE but Tbird would be the main use one