I have observed that in some orgs, some Apex tests will fail if those tests run in parallel with other tests, but will pass if the same tests do not run in parallel. I tried to find information from Salesforce that describes in detail what information/context is shared between Apex tests and all I could find is this:
Sometimes, parallel test execution results in data contention issues, and you can turn off parallel execution in those cases. In particular, data contention issues and UNABLE_TO_LOCK_ROW errors might occur in the following cases.
Can someone explain what data/context is shared between individual tests when executed in parallel?