You can be signed in on more than one device at the same time -- your phone and a tablet, for example.
What’s shared. Everything linked to your account: your workouts, your nutrition, your progress, your messages. If you log something on the tablet, it’s on your phone too.
What differs per device. Settings that are about this device: which screen the app opens on, when your week starts, which gym is active, and whether notifications are on. Those deliberately don’t move across.
Signing out. At the bottom of Profile. Your data stays; you only sign out on this device. When you sign out, this device’s notification key is deleted, so your messages don’t go to a phone that may now belong to someone else.
Lost your phone. Change your password. Also get in touch if you suspect someone else can access your account.
Signing out doesn’t erase anything. Everything is ready again as soon as you sign back in.