This is more a mathematical concept than programming.
Just as a square is a particular case of a quadrilateral, an array is a particular case of an array: it is a matrix with only one dimension. We understand array as a synonym for vector.
In programming the Array type is a data structure whose elements can be manipulated through indexes and can have one or more dimensions.
The terms vector and matrix, by analogy to mathematics, are sometimes used to denote two-dimensional arrays and two-dimensional arrays, respectively.
There are some controversies about this, but I will say what is most accepted.
A vector is an array of one dimension only, that is, it has only one row or one column of data. Normally we use the term matrix when there is more than one dimension, then it has at least rows and columns, it may have other dimensions.
In other words matrix is a multidimensional vector.
There is the vector vector that is often confused with array, but it is not, after all, the sizes of each row or column is variable, an array holds everything of the same size, holding the "rectangular drawing".