The terms yoga and karma-yoga are occasionally used interchangeably by Śaṅkara, especially contrasted with the jñāna-yoga of Sāṅkhya. He defines Yoga in II.39.
Yoga, the means to that (Knowledge), is:
(1) first, distancing oneself (reading prahāna with Ānandagirl and not prahanana ‘killing’) from the pairs-of-opposites (dvandva);
(2) undertaking actions as karma-yoga, namely as worship (ārādhana) of God;
In IV.38, ‘purified by yoga’ is glossed as purified by karma-yoga and samādhi-yoga. The accompanying word mumukṣu presumably would cover dvandva-prahāna.
In XII.12 and elsewhere, karma-yoga is used as yoga, to include other elements besides action:
Yoga is said to be samādhi – concentration on the Lord (Īśvare cetah-samādhāna), and a performance for the Lord’s sake of actions, and so on. It rests on seeing difference between Self (ātman) and the Lord (ātmeṣvara bheda āsritya)…. It is not compatible with Right Vision (samyag-darśana-ananvita)…. It relies on an Īśvara apart. So jñāna-yoga, which knows the Lord to be the Self, is not practicable for a karma-yogin…. Conversely, the jñāna-yogin, who sees no difference between them, would have no incentive to rely on a supposedly purely external Lord.
Nevertheless, though (as Śaṅkara points out) the Lord directs Arjuna (in IV. 15) to karma-yoga, this is after his first teaching of jñāna, in chapter II, has had no effect. jñāna yoga has been taught to Arjuna, but he could not then follow it.
In X.19 the Lord specifically consents to Arjuna’s request, by declaring: ‘I will tell you of my glories’, For constant meditation (nitya dhyeya) says Śaṅkara, and adds: ‘Listen!’ The first of these glories is: T am the Self (aham ātmā) in every living being,’ which is a statement of jñāna . Then, for one who cannot meditate on the Lord as Self (tad-asakta), the glories of the Lord immanent in Māyā are given.
Later in X.37 it is even more direct: ‘I am Dhanañjaya’ (Arjuna), but Arjuna fails to take it in (though for a moment he thinks he has). So in fact instruction in jñāna is given, but while Arjuna’s basic feeling is that of karma-yoga, he cannot be rightly said to be on the jñāna-yoga path.