Mechanical engineering, most mid size or large orgs use "PLM" software (product lifecycle management) to handle "versioning" (revisions, change orders, etc) of CAD files, drawings and sometimes other engineering documents.
They tend to be complex, expensive and centralized software that require an entire IT team to set up and maintain. Sort of similar to ERP software, and in fact, they often get integrated with ERPs.
Smaller orgs tend to use nothing, or an ad hoc system of file/folder structures and spreadsheets, because they can't justify the cost of PLM. I wish there existed a lightweight option. Git doesn't work well with large binaries and it's merge-based workflow doesn't really apply to CAD anyways. PLM software usually use an exclusive check-out model. There is OnShape, a low cost cloud CAD start-up that was bought by Siemens, which has some PLM features I believe.