What’s the difference between “version number” in iTunes Connect, “bundle version”, “bundle version string” in Xcode?

Yes, they are related. They all refer to the version of your application.

• iTunes Connect
  This is the version number shown in the App Store; This must be a pure version number like 1.2.3

• Bundle Version (CFBundleVersion)
  This doesn’t need to be a pure version number. This can be something like 12345 or 1.2.3 (Build 12345AB). This is shown in the About window for Mac OS X apps for example and is often more a “Build Number” than a “Version Number”.

• Bundle Version String (CFBundleShortVersionString)
  This value is used as the “real” version number. This must be the same string as used for the version in iTunes Connect.

Update:
As pointed out by @snlehton, the CFBundleVersion has to be a pure version number like 1.2.3 when you want to upload your application to the (iOS) App Store.