When one studies electrostatics we have the electric field $\mathbf{E}$. This object usually is introduced as a field produced by a configuration of charges such that the force on another charge $Q$ at the point $a\in \mathbb{R}^3$ is $\mathbf{F} = Q\mathbf{E}(a)$.
In magnetostatics, one also has a field $\mathbf{B}$, but in the case it allows the force on a charged particle be written $\mathbf{F} = Q\mathbf{v}\times \mathbf{B}$. Although the velocity dependence thing, it is also one vector field that allows the magnetic force be obtained based on it, like the electrostatic field.
Although this similarity, I've seem in many places people calling $\mathbf{B}$ the magnetic induction field rather than magnetic field. Why is that? Is that just a terminology that has been established by convention or there is really a difference between being "a magnetic field" and "a magnetic induction field"?
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