When development team provides the build the build release team deploys the build in test environment. In some companies test team deploys the builds in test environment depending on the team's responsibilities.
Builds usually will be ear(enterprise archive) file or a war(web archive) file. A web application is a 3 tier architecture and depends on where the code changes are done accordingly the builds are deployed on the respective servers
war file is deployed on web server and ear file on application server.
Websphere provides the option to deploy both ear & war builds. Other servers do not provide the same feature.
FYI - There is rar file(resource archive) which is resides within ear and usually used to connect siebel, SAP or 3rd party/legacy system or adapters