In the original BGV paper, the ciphertext contains just one component, whereas here in the library, the BGV implementation as well as in other libraries has 2 ciphertext components per ciphertext. Why is this difference? am I missing something.

The original BGV paper might assume LWE (actually, GLWE), while 2 components is usually two polynomials, thus RLWE. Perhaps you might look at this

I am not aware of any “BGV” scheme where the ciphertext includes only one polynomial. Can you share a link to the paper you are referring to?

Perhaps they refer to the basic LWE version of BGV, where a ciphertext is a vector {\bf c} \in \mathbb{Z}_Q^n encrypting a single message [\mu]_t ?

The original paper Here has just 1 ciphertext component (not polynomial but vector) for the basic scheme (page 7) and leveled scheme (page 11). That’s what confuses me. I know this is the GLWE representation but do not understand how this changes to two components in RLWE space

The paper uses a generic representation that works for both LWE and RLWE rings. Read the first paragraph in Section 2.3 which states the generalization. In the case of RLWE, n=1 and R_q=\mathbb{Z}_q / f(x^d+1), and the encryption in Section 3.1 generates a ciphertext in R_q^2, that is, two components.

Similarly, in the LWE case, where n=poly(\lambda) and R_q=\mathbb{Z}_q, the ciphertext has two components as well: a vector in \mathbb{Z}_q^n and an integer in \mathbb{Z}_q.