Hi Pablo Gonzalez, one way to resume this would be:

Chat is a channel and/or Zendesk product which we can enable as a channel on our legacy/classic widget.
That said, Web widget (classic) is the legacy widget that has existed for years (previously Zopim).
Web widget is the 'new normal', it includes more customizations, Flow Builder integration etc.
Messaging is a replacement for the Chat channel. It's the new chat UX embedded in the default Web widget (i.e. not available in classic web widget)

Hope this clarifies things a bit, I understand how it can be a bit confusing :-)