Does Ohm's law $V = IR$ mean voltage causes current, or does it just say that voltage and current are related?

As usefully pointed out in the comments, Ohm's law just states that voltage $V$ and current $I$ have a relation. Therefore, Ohm's law per se means equivalence and not causation. This could be not immediate to deduce, there is plenty of Physics laws which imply both a relation and a causation, but this is not the case for neither Ohm's law, nor Newton's second law, as you correctly mentioned.

The causation is established according to the specific circuit and its features.

For example, a battery is a device which tries to always impose a fixed voltage $V_b$ between its terminals $V_+$ and $V_-$. In this example, $V_b$ is the cause and the independent quantity. If you connect a lamp between the battery terminals, it can be represented as a resistance $R_{\mathrm{lamp}}$. The voltage across $R_{\mathrm{lamp}}$ is $V_b$. The current on $R_{\mathrm{lamp}}$ is then the effect of the presence of the battery, and the dependent quantity. This is a little circuit which consists in a voltage generator (the battery), a resistor (the lamp) and a single loop. As an effect of the imposed voltage, a current $I$ will flow through the resistor. $I$ is the dependent quantity: to determine its value, you must know both $V_b$ and $R_{\mathrm{lamp}}$; Ohm's law can be written as

$$I = \frac{V_b}{R_{\mathrm{lamp}}}$$

Of course, the battery may not be able to erogate enough current to create or maintain a $V_b$ across $R_{\mathrm{lamp}}$, or the current may be so high that $R_{\mathrm{lamp}}$ is damaged, and so on, but these real cases are not relevant here.

On the other hand, transistors can be used as current generators in several configurations. Current generators try to always impose the value $I_b$ of current between their terminals $I_+$ and $I_-$. If you connect a resistor $R_{\mathrm{lamp}}$ between these two terminals, you already know the current $I_b$ flowing into the resistor: $I_b$ is the independent quantity and the cause. This is again a simple circuit consisting in a current generator, a resistor and a single loop. As an effect of the current $I_b$, a voltage $V$ will appear across the resistor: in this case, $V$ is the dependent quantity. To determine its value, write Ohm's law as:

$$V = R_{\mathrm{lamp}} I_b$$

There are again some real scenarios when $I_b$ can not be imposed by the current generators, but they can be discarded here.

The same Ohm's law is used in both the examples, but with exchanged roles between $V$ and $I$, according to the circuit.

In any circuit, regardless of its structure, if you know the value of a resistor $R$ and the current $I$ flowing through it, you can determine the voltage between the resistor terminals as $V = RI$. If instead you know the voltage existing between the resistor terminals, you can determine the current as $I = V / R$. In the previous cases, the cause was always the independent quantity and the effect was the dependent quantity. In this case instead, you don't know what is the cause, but you can still use Ohm's law: the dependent quantity is now, for you, the one you still do not know.

As correctly pointed out by Whit3rd's answer, Ohm's law mainly refers to a resistor in a circuit and it involves three quantities: the voltage across it, the current through it and the resistance value. If you know two of them, regardless of what is the cause and what the effect, you can determine the third one.

In circuitry, there are materials that conduct electric current. While that is useful, it is NOT the only way that currents come about: an electron beam in a vacuum, or a charged belt motor-driven in a van de Graaff machine, do not have a material conductor, nor any associated 'R' constant.

If a conductor with one end grounded has voltage source applied to its other end, or has a current source connected to it, the resistance of that conductor does relate the current and voltage according to Ohm's law (with very minor exceptions). That relationship tells us about the resistor, but not about the causation of a current-is-flowing episode. Knowing both the resistor AND one of (voltage-difference, current), we can calculate the third variable.

And, it works the third way, too. Knowing a voltage applied and how much current passes, we can compute a resistance.

Three unknowns, and one equation given by Ohm's law. Two measurements (two more equations) and you can solve for all three variables.

the law of Ohm just means equivalence and that voltage is not the cause

Yes, that seems correct. Does generator voltage drive a resistive light bulb, or generated current? Both are equally valid statements.

The potential difference, or voltage, between two points is defined as the work per unit charge required to move the charge between the points. So the voltage across the resistor is the work required per unit charge to move the charge through the resistor. Since power in a resistor is $i^{2}R$, for a current of 1 ampere (1 coulomb per second) and resistance of 1 ohm, we have 1 watt (1 joule per second) of work. After 1 second, 1 joule of work was done to move 1 coulomb of charge through the resistor. That work represents a drop in potential.

Some voltage source was needed to establish the current in the circuit where the resistor is used. But unless that source was connected directly across the resistor (with no other circuit elements in series), the voltage across the resistor was not the "cause" of the current through the resistor. It is simply, as others said, the relationship between the current and resistance, $V=IR$.

Hope this helps