DevOps is the concept and practice of no longer keeping IT development and operation teams separate from each other. And instead essentially integrating the two teams into a single elite team where IT engineers can work much more efficiently and cohesively across the entire life cycle of a project, from early development to testing and deployment. IT engineers in this team possess and develop a wide range of skills that are not specific to one project or one development point in a projects life cycle.
DevOps teams are constantly evolving to meet new demands in the market and are ever using new and evolving technologies to speed up and automate processes in a development cycle that were historically a manual and time-consuming task. These new tools help DevOps teams move a project along with high velocity and help engineers independently accomplish tasks whilst maintaining high levels of quality and security due to the wide range of skills that a DevOps engineer posseses and the merging of development and operations teams.
WebOps is a sub-team within DevOps and focuses more on the monitoring and daily operations of web applications.
WebOps covers most areas of infrastructure such as networking, security and database administration and because of this, WebOps engineers can naturally progress down the path that interests them the most while still having a broad knowledge of the other types of infrastructure.
Overall, if you need to build a web application from start to finish then a DevOps team will be right for you. However, if you already have a fully-functioning web application and just wish to host and maintain your web application then a WebOps team will be best suited for this job.