I think you're asking why there are tax credits and tax deductions.

Deductions reduce the amount you're liable for.

Credits act as if you already paid that much in.

You’re missing OP’s point. Some credits are refundable and others are not. Credits are deducted from taxes due, but some can take the amount due below zero resulting in a refund (or increased refund), whilst other cannot.

Deductions reduce income, before tax.

Could be a number of things. One significant consideration is whether we want the government to more fully fund certain things versus potentially limited funding where a tax credit is capped at taxes owed. The Earned Income Tax Credit for example is fully refundable, and in many situations, there's the potential for not only paying zero federal taxes, but getting additional funds from the government as well. The EITC is a welfare program of sorts, and while it's hard to get into the minds of policymakers, it's likely far more efficient to distribute all these funds directly as part of the tax filing and refund process rather than knocking tax liability down to zero and then having a second program to process the remainder of the "unused" funding that the government is willing to pay to EITC filers.

A non-refundable tax credit however, serves as an incentive to spend (or do whatever is necessary to earn the credit) only insofar as you have tax liabilities that equal or exceed the credit. While we can try to attribute some rationale to how policy and rule makers determine which are refundable and which aren't, it likely comes down to lobbying and the need to meet projections.

Each tax credit in the US's baroque tax system is added via a new law, and is negotiated independently from all the others. So whether any given one is refundable depends on the specific horse trading at the time it's enacted.

Most tax credits are nonrefundable, meaning they can reduce the tax you owe, but if it's more than you owe, any excess just disappears. It's easier to get approved, because the cost is capped that way.

This type is often used to encourage some behavior or act, like installing solar panels or buying an electric car.

A few tax credits, mostly directed at low income tax payers, are set up as refundable to benefit the folks who need it most.

Some will carry the balance year over year until it's been deleted too.

Think of it like coupons vs. promotional gift cards given out by a grocery store. They use coupons in a situation where they want to encourage you to do something (buy X product), but want to limit the cost to themselves—the maximum discount is 100%. This is analogous to a non-refundable credit.

With a gift card giveaway, they’re saying the situation is such that they want to give you more money to spend, because that’d be better for everyone. This would be analogous to a refundable tax credit, which is mostly aimed a people with lower income, because helping them make ends meet and maybe even have a little extra to spend is better for everyone in the grand scheme of things.