Electromagnetism was developed in the mid-19th century, culminating in work of Maxwell and Heaviside (q.v.), starting from previous work by Faraday and others.
Current is a scalar, with a positive or negative sign.
It is defined in physics as an integral over an area of the scalar product of the current density vector and the area vector normal to the area.
This was before the electron was discovered in 1897, and shown to have a negative charge using the existing definition of voltage and current polarity.
As can be found in elementary textbooks, the flow of electrons is one form of current, but the flow of positive ions is also an electrical current.
The easiest forms to consider are electrons through a vacuum tube, or ions in a particle accelerator vacuum: current through solids (copper and semiconductors) is a more complicated process (solid-state physics).
I think of current in a wire as a slight tendency of a gazillion electrons to move to the right, making a current flowing to the left, as a result of a voltage gradient along the wire.