Here, Shree Krishna uses the word
sānkhya
to refer to
karm sanyās
, or the renunciation of actions with the cultivation of knowledge.  It is important to understand here that renunciation is of two kinds
phalgu vairāgya
and
yukt vairāgya
.
Phalgu vairāgya
is where people look upon the world as cumbersome, and renounce it with the desire of getting rid of responsibilities and hardships.  Such
phalgu vairāgya
is an escapist attitude and is unstable.  The renunciation of such persons is motivated by the desire to run away from difficulties.  When such persons encounter difficulties on the spiritual path, they become detached from there as well, and desire to run back to worldly life.
Yukt vairāgya
is where people see the whole world as the energy of God.  They do not see what they possess as belonging to them, and do not wish to enjoy it for themselves.  Instead, they are motivated by the desire to serve God with whatever He has given to them.
Yukt vairāgya
is stable and undeterred by difficulties.
The
karm yogis
, while conducting their daily duties externally, develop the sentiment of
yukt vairāgya
, or stable renunciation.  They see themselves as the servants and God as the enjoyer, and hence they become fixed in the consciousness of doing everything for His pleasure.  Thus, their internal state becomes the same as that of the
karm sanyāsīs
, who are completely absorbed in divine consciousness.  Externally, they may appear to be worldly people, but internally they are no less than
sanyāsīs
.
The Puranas and Itihās relate the examples of great kings in Indian history, who, though externally discharging their kingly duties with diligence and living in royal opulence, were mentally completely absorbed in God-consciousness.  Prahlad, Dhruv, Ambarish, Prithu, Vibheeshan, Yudhishthir, etc. were all such exemplary
karm yogis
.  The Shreemad Bhagavatam states
gṛihītvāpīndriyair arthān yo na dveṣhṭi na hṛiṣhyati
viṣhṇor māyām idaṁ paśhyan sa vai bhāgavatottamaḥ
(11.2.48)
“One who accepts the objects of the senses, neither yearning for them nor running away from them, in the divine consciousness that everything is the energy of God and is to be used in His service, such a person is the highest devotee.”  Thus, the truly learned see no difference between
karm-yog
and
karm sanyās
.  By following one of them, the results of both are achieved.