Meaning of the notation $\ll$, as in $ |\zeta(\sigma+it)|\ll\left(\frac{t}{2\pi}\right)^{\frac{1}{2}-\sigma} $

Question

In number theory I often see the notation $\ll$ intuitively meaning "way smaller". I first though it had the same meaning as $o$ but then I came accross expressions like $$ |\zeta(\sigma+it)|\ll\left(\frac{t}{2\pi}\right)^{\frac{1}{2}-\sigma} $$ for $\sigma<0$. There, there are $2$ parameters involved : $\sigma$ and $t$ so the $o$ analogy doesn't apply there, except if $\sigma$ is fixed. But even if $\sigma$ is fixed we don't know wheter it should be $$\underset{t\rightarrow+\infty}{o} \qquad \text{or} \qquad \underset{t\rightarrow -\infty}{o},$$ or even something else. That's why I'm asking what is the definition of $\ll$ and how can it be used. For instance does $f(x,y)\ll g(x,y)$ is as allowed as $u_n\ll v_n$.