There’s a separate public/private keypair for every bitcoin address. You don’t have a single private key that unlocks everything. Bitcoin addresses are a 160-bit hash of the public key. The chance of a collision is astronomically small.
The keyspace is so large that it’s beyond what we can comprehend. Even if every person on earth generated a new key every second for the age of the universe, the probability of any two people generating the same key would still be effectively zero.