Concourse and Jenkins can be primarily classified as "Continuous Integration" tools.
Concourse: Pipeline-based CI system written in Go.
Concourse's principles reduce the risk of switching to and from Concourse, by encouraging practices that decouple your project from your CI's little details, and keeping all configuration in declarative files that can be checked into version control;
Jenkins: Jenkins is built in Java.
It is an extendable open source continuous integration server and is one of the leading DevOps tools for continuous integration.
It provides over 300 plugins to support building and testing virtually any project.
"Real pipelines" is the primary reason why developers consider Concourse over the competitors, whereas "Hosted internally" was stated as the key factor in picking Jenkins.
Hope this helps!