That would be Ready from the position of shoulder arms. In all the CW manuals, the first firing is at shoulder. In Gilham and Baxter, the weapon is presented and cocked as part of the Ready. See para. 117 of Gilham. For subsequent firings, the weapon remains in the prime position after loading and is, by definition, the Ready. See para. 116 of Gilham.
I could see how one could be called the high ready and the other the low ready. Theyre not period terms.
As a rule, reenactors don't differentiate between first and subsequent firings. The reason is that they have been taught to "come to the shoulder when ready" after loading even though the manuals all say to remain in the prime position after loading for the subsequent firings at that location. Should the troops march to a new location, they presumably go to shoulder arms and are halted. Being at shoulder, they would now execute the Ready per the appropriate manual. For Gilham, it would be presented and cocked. For Hardee and Casey, it would be readied and cocked.
Is the original question being asked because of the manuals being used for the upcoming On To Richmond?