In economic policy, the difference between the left and the right is a question of how equality is best achieved. For the left, the role of the state in economic affairs is to act in a manner than ensures equality of the distribution of resources. This is an active role that utilizes state functions in a manner that promotes the welfare of the downtrodden and disadvantaged. In contrast, the right seeks equality of opportunity by eliminating barriers that prevent folks from engaging in the economic marketplace.
I don't think either of these claims is really true.
The left is traditionally marked by policies which seek to redistribute wealth, but that does not imply a support for strict equality. The British NHS, for example, is a classically left-wing institution, but it operates on a thoroughly unequal basis, being funded on the basis of ability to contribute, and distributing on the basis of need for its services.
The right has in the 20th century been marked by an opposition to economic regulation, but that doesn't imply a support for "equality of opportunity". Until Thatcher, British conservatives were explicitly
opposed to equality of opportunity, holding instead to a sort of sloppy functionalism in which each social stratum should know its place, and get on as best it could within those terms. (This becomes doubly obvious if we go back to the 19th century, when free trade was a key plank of the British left, in opposition to the protectionism of the conservatives.)
Instead, I think the distinction is, as I said before, about orientation towards power. The left pursues policies policies which undermine the power that one individual is able to wield over another, which in capitalist society primarily take the form of deep wealth inequalities; socialised healthcare, for example, removes the power imbalances inherent in a privatised system as we see in the US. The right pursues policies which defend power; demolishing market regulations while bolstering protections for private property allows the power of capital to operate unhindered.