There is issue in key encapsulation when you say "Bob generates his own secret key and encrypts it using Alice's public key. He sends the result to Alice."

This is encryption not encapsulation. In key encapsulation algorithm, the secret key to be shared by Bob is produced as an output of the “encapsulation” algorithm, which is run on the Alice public key alone. This works as follows:

The input of encapsulation algorithm is the Alice public key and output generated by the encapsulation algorithm on Bob side is the ciphertext c and secret key k. Now, Bob will send ciphertext c to Alice and Alice will decapsulate it with its private key to recover the secret key k.

For more concept clarity see the peikert's KEM and its more clear version by Vikram using lattice based cryptography in post-quantum cryptography. ).

There is issue in key encapsulation when you say "Bob generates his own secret key and encrypts it using Alice's public key. He sends the result to Alice."

This is encryption not encapsulation. In key encapsulation algorithm, the secret key to be shared by Bob is produced as an output of the “encapsulation” algorithm, which is run on the Alice public key alone. This works as follows:

The input of encapsulation algorithm is the Alice public key and output generated by the encapsulation algorithm on Bob side is the ciphertext c and secret key k. Now, Bob will send ciphertext c to Alice and Alice will decapsulate it with its private key to recover the secret key k.

For more concept clarity see the peikert's KEM and its more clear version by Vikram using lattice based cryptography in post-quantum cryptography. ).