Qi Condensation (凝气 níngqì) – also known as Qi Refining (炼气 liànqì) or Qi Gathering (聚气 jùqì). An initial stage of cultivation which involves absorbing Qi from the natural world and refining it inside the body.
Foundation Establishment (筑基 zhùjī) – also translated as Foundation Building. The stage after Qi Condensation. Once a cultivator's Qi crosses a certain threshold (in the volume and/or density of the Qi), they'll be able to breakthrough to this stage.
Golden Core Formation (结丹 jiēdān) – sometimes left untranslated as "Jiedan". The stage after Foundation Establishment. It involves forming a Golden Core (金丹 jīndān) by using the Dantian as a crucible and the Cultivation Base as raw material.
Nascent Soul (元婴 yuányīng) – sometimes left untranslated as "Yuanying". Literally translates as "Origin Infant". The stage after Core Formation . The Nascent Soul resembles an infant or miniature person and resides in the Dantian, typically sitting in a meditative position. The Nascent Soul can travel outside the body and is like a second life for cultivators – if their main body dies, their consciousness can continue to exist in the Nascent Soul.
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Ranks / Levels / Layers (级 jí) (层 céng) – a common way to quantify martial power or the progress made in cultivation. In many cases (although not all) where these are used, there are 9 ranks/levels/layers to each stage of cultivation, with rank 1 being the start and rank 9 being the peak. After breaking through to the next stage, the practitioner starts at rank 1 of that new stage. The number 9 has a great deal of symbolism.
Another set of commonly used terms are Early-stage (初期), Middle-stage (中期), Late-stage (后期) & Peak (巅峰). For example, someone might be a "late-stage Core Formation expert" or they could be at "the peak of the Nascent Soul stage".A half step to __ (半步__境) – refers to someone who's infinitely close to breaking through to the next stage of cultivation, but hasn't achieved it yet. For example, someone who's "a half step to Foundation Establishment" is still technically at the Qi Condensation stage, but they're only a hair's breadth away from Foundation Establishment.