Marketplace (ACA) plans are sold on the government exchange, come with income-based subsidies, cover the ten essential health benefits, and can't turn you down or charge more for a pre-existing condition.
Private health plans are sold off the exchange. They're typically medically underwritten, which means your health history affects whether you qualify and what you pay, and they may limit or exclude pre-existing conditions and cover less than an ACA plan does. In exchange, they often offer broader networks, lower premiums for healthy applicants, and enrollment outside open enrollment. They are not available in every state, and in a handful of states they don't satisfy the individual coverage requirement.
Which one fits depends on your income, your health history, and what you need covered. We'll walk you through both honestly, including the trade-offs.