In a democracy, the government is an outcome of elections, however they represent the majority and you may not be in that majority. This is why you can't talk about democracy without a strong culture focusing on the individual's rights, aka liberalism, otherwise all you have is a tyranny of the majority.
You're also deeply wrong. The fundamental difference between a state and corporations is that the state has a monopoly on violence and anything that a corporation is doing, and that harms individuals, can only happen with the complicity of the state. For example, there is no such thing as a natural monopoly, all monopolies are granted by the state in one way or another.
And the differences should be obvious, given the state can deprive you of freedom, it can starve you, it can inflict physical violence, and can even kill you. Corporations can't do this, unless the state commands it, obviously.
> It may be harder to influence corporations.
Actually, depriving Apple of the money you'd pay for an iPhone has more impact that your democratic vote. And even if you disagree with this, consider that you can vote for politicians promising to regulate Apple. And switching to Android or Windows has a lower cost than switching countries (and yes, that's an oligopoly, but that's because your state granted it via IP laws).