Luke wrote:So in reality, in modern China and Taiwan, there is little difference between a Chan monk who is a Linji lineage holder and a Chan monk who is a Caodong lineage holder? (Both Chan monks have probably studied mostly the same things.) Is this correct?
There are just monks (and nuns, in fact, a lot more nuns than monks in Taiwan). Whether they say they belong to this or that lineage (that includes even Tiantai, Huayan or anything else) is usually not relevant, because it is often defined by what monastery they were ordained or live in. For instance, Ven. Xingyun of Fo Guang Shan is Linji lineage but there isn't anything Linji (or even Chan) specific in his teachings. And while Ven. Shengyan has created the Dharma Drum lineage (combination of Linji and Caodong), his teachings are a mixture of Tiantai, Humanistic Buddhism and a bit of Japanese Zen (but mostly his own system), while at the same time in the Western Chan Fellowship (followers of Ven. Shengyan) they teach a mixture of Soto Zen, huatou practice and some sort of therapeutic techniques (just to show how Western perception and presentation can be quite different even if there is a direct relationship). Korea is another good example here, since the majority of monks belong to a single church, the Jogye Order, that actually promotes Ganhwa Seon (i.e. Linji style Chan), but individual monasteries and teachers can transmit very different things (even rejecting Ganhwa practice).
The sort of "objectless meditation" is called mozhao (silent illumination, mokusho in Japanese), just as Ven. Shengyan uses it. Interestingly, it was originally a derogatory term used by Dahui. That is, mozhao used in the Caodong context. Otherwise it can have many other names, like no-thought, no-mind, prajnaparamita, one act samadhi, etc.