Is a line bivector the same thing as a vector? In the abstract of this article, the author said the following:

An element of this vector space will be called a line bivector.

According to wiki,

..., a vector space (also called a linear space) is a set of objects
called vectors, ...

So, if a line bivector is an element of a vector space, then a line bivector must be a vector since all the elements of a vector space are vectors. Am I correct?
PS: I'm a complete amateur in linear algebra.
 A: Yes, you are technically correct that bivectors are also vectors in the sense that they live in a vector space. The issue here is that there is a conflicting use of terminology: in some contexts (particularly differential geometry and in physics), the term "vector" only refers to members of a particular type of vector space, while "bivector" then denotes something different, related to the first fixed vector space.
For example, in these contexts, "vector" might specifically refer to an element of $\mathbb R^n$, i.e. an $n$-dimensional Euclidean vector, while then bivector refers to a linear combination of terms of the form $e_i\wedge e_j$ where $e_i$ are basis vectors for $\mathbb R^n$ and $\wedge$ denotes the exterior product.
An analogy: the term "scalar" is typically used when we already have a vector space $V$ fixed over a particular field $K$, where elements of this base field $K$ are then called scalars. This is a relative notion to the vector space $V$. So, for example, it is true that $\mathbb R$ is a vector space over itself, so elements of $\mathbb R$ can be called vectors too --- but in some contexts, such as in physics, you normally think of real numbers as scalars. Similar is true for "bivector", this is also used when the first vector space $V$ is already fixed in mind.
