Halq is shaving the head completely, and taqsir is trimming the hair — cutting at least a fingertip's length from all or most of it. Both mark the completion of the major rites, ending most of the restrictions of ihram, and both are described in the Quran's promise to the believers before the Conquest: "...with your heads shaved and [hair] shortened, not fearing" (48:27).
For men, either option is valid, but the Prophet ﷺ showed a clear preference for shaving, supplicating for those who shaved their heads three times and for those who merely trimmed only once (Sahih al-Bukhari 1727) — indicating shaving carries greater merit, though trimming is fully acceptable, especially for a pilgrim planning to perform Umrah again soon after. For women, the ruling differs: by scholarly consensus, women only trim a small amount, roughly a fingertip's length, gathered and cut from the ends of the hair; shaving the head is not permitted for women in this context. This is typically the final act of ihram, done after tawaf al-ifadah and sa'i, or after stoning on the 10th if hair-cutting is done in Mina.