I'm a newer to the lattice theory, so there is a basic notion about "full rank" confusing me.

In some papers focusing on the lattice theory, they always use the full rank lattice (the number of basis vectors $m$ is equal to the dimension $n$ of the space $\mathbb{Z}^n$) as the research target, such as generating a hard lattice with short basis, solving some lattice problems. However, In some lattice problems, including SIS and LWE, they always introduce a random matrix $A$ with $m=poly(n)$ as basis vectors.

Therefore, I am confused that why the matrix $A$ in SIS and LWE is not full rank?