Originally CNN was used for Cellular Neural Networks and ConvNet was used for Convolutional Neural Networks. However, lately, CNN and ConvNet are both used interchangeably for Convolutional Neural Networks.
One of advantages of using google products now is that all of their products can be controlled with a single account without much hassle. Since one is going to use at least one of their products, it makes to use Gmail. Gmail has a lot of advantages, although Fastmail does provide more flexibility.