What’s the difference? Think about when a project fails. “Bad things” happen for the person accountable, whereas the person responsible can move on to the next project. The buck stops at the accountable individual not the responsible one.
In practice, every project has a manager that’s accountable and a lead that’s responsible. As ICs move up the ladder, they’re able to lead larger and larger projects and offer expertise and guidance across multiple projects. Think: providing feedback, from hard-fought past experience, on a design doc that’ll save a team 3 months worth of effort; architecture review, etc. Essentially ensuring and instilling engineering excellence across the organization.
One thing to note, moving up into a senior engineering role may mean you’ll be coding or designing less. And that’s to be expected. Senior engineers understand that coding/designing is one portion of a larger picture that includes communication, eliciting buyin, documentation, architecture, software quality attributes, and many more responsibilities.
In theory, this provides equal management and IC tracks that are fulfilling to all. In practice, very few companies work this way, but there are some out there. And when you find them, you won’t want to leave because it’s such a pleasant experience.