Energy is conserved. Charge is conserved. And, with a few simplifying assumptions, current is equal everywhere in a series circuit, and the voltages across parallel components is equal.
While still conforming to these rules, there are electrical machines that trade current and voltage between an input and an output. The transformer is one such machine, but there are others. For an ideal transformer, power in equals power out, but the ratio of voltage between sides is equal to the transformer's turns ratio, and the current ratio similarly different such that energy is conserved. For non-ideal transformers (and indeed most real power converting machines), some of the input power goes into losses in the converter, and usually manifests as heat.
You could consider this as converting voltage into current, or not, depending on how you define converting. Does a car transmission convert torque into angular velocity? If so, a transformer does convert voltage into current.
There are many mechanical machines analogous to a transformer. Gears, levers, pulley systems, turbines, etc. Anything that affords mechanical advantage is a good example. All machines are subject to the law of conservation of energy. As long as they also have no means to store energy, that means power in equals power out. Mechanical power is the product of force and velocity:
$$ P = Fv $$
which is why if you want to use one of these mechanical advantage machines to apply more force to lift a thing, you will also lift it more slowly. Or, if you want to lift a thing quickly, you must also apply more force.
Perhaps then it's no mistake that electrical power is the product of voltage and current:
$$ P = VI $$
and voltage is how hard something is pushing on charge, and current is how fast that charge is moving.