"Say which one is true."
Fact Two: Apple Has Processed It
An upload is only the start of App Store Connect's work. The build has to be processed before it appears for testing, and App Store Connect sends an email when that finishes. This is also where the late refusals from the gate lesson surface: an ITMS notice arrives by email about a build whose upload line was green. And a build whose export-compliance question is unanswered waits in App Store Connect until someone answers it, which is why family apps declare ITSAppUsesNonExemptEncryption in their Info.plist. Until the email or the TestFlight page says processed, fact two is unknown, whatever the log says.
Fact Three: The Group Has It
Internal testers belong to groups. When a group is created with Enable automatic distribution, builds uploaded from Xcode tooling go to every member of that group on their own; without it, every build must be added to the group by hand, and a build that nobody added is processed and still unreachable. The group's build list is where fact three is read. Family apps use one internal group each with automatic distribution on, so fact three normally follows fact two within minutes, but it is still checked rather than assumed.
Fact Four: It Is on the Device
App Store Connect's tester list shows a status per tester: Invited, Accepted, and Installed, which means the tester downloaded the build. The most direct reading is the device itself. Family phone apps show their marketing version and build number in settings, read from the running app's Info.plist, so "installed" is a number seen on the phone, not a conclusion drawn from a green pipeline. The TestFlight app on the device can install updates automatically when the tester has that turned on, and until it does, the old build keeps running.
Installed is delivery of the app. It is not always delivery of the change. When a client change depends on a new engine route, the engine at home has to be restarted as well, or the newly installed app meets an older engine, which is exactly how a correct capture came to be parked with "Method Not Allowed".
Writing the Report
A delivery report lists the four facts with evidence for each and a status line that names the highest fact actually verified. It does not say "shipped" when it means uploaded, and it does not say "on the phone" when it means assigned. A build becomes untestable 90 days after upload, so a long-running tester needs a fresh upload before then, even when nothing in the app has changed.