It varies.

Historically, you're right about domestic first class--which was similar to what's sometimes sold as premium economy these days.

However, some airlines (e.g. United) do sometimes have, in United's case, Polaris seating in business/first which is similar to/same as lie-plat Polaris seating in international. AFAIK, United just has the single Polaris class and doesn't have a separate first class like some airlines do.