Lex is the same technology used to power Amazon Alexa. It utilizes ASR (Automatic Speech Recognition) to convert speech to text, it can recognize intent and is commonly used to power chatbots and automated call center bots.
Connect is a cloud based virtual contact center that allows you to accept calls and create contact flows, this is a interface where you can alter the user experience through a drag and drop interface to play certain messages, request certain information depending on which path they’ve taken, etc.