kamyanam karmanam nyasam
sannyasam kavayo viduh
prahus tyagam vicakshanah
The Supreme Personality of Godhead said: The giving up of activities that are based on material desire is what great learned men call the renounced order of life [sannyasa]. And giving up the results of all activities is what the wise call renunciation [tyaga].
Commentary by Srila Prabhupada
The performance of activities for results has to be given up. This is the instruction of Bhagavad-gita. But activities leading to advanced spiritual knowledge are not to be given up. This will be made clear in the next verses. In the Vedic literature there are many prescriptions of methods for performing sacrifice for some particular purpose. There are certain sacrifices to perform to attain a good son or to attain elevation to the higher planets, but sacrifices prompted by desires should be stopped. However, sacrifice for the purification of one’s heart or for advancement in the spiritual science should not be given up.
Commentary by Sri Visvanatha Cakravarti Thakur
Taking up the former idea first, the Lord explains the different derivations of the two words. To renounce (nyasa) at the very root activities performed for fulfilling personal desires (kamyanam karmanam) is called sannyasa. Personal desires are indicated in such statements as the following:
putra-kamo yajeta, svarga-kamo yajeta
One with a desire for a son should worship. One with desire for svarga should worship. Apastambha Srauta Sutra 3.9.4,19.10.14
This does not mean that one should reject daily obligatory activities (nitya karma) such as sandhya worship.
Tyaga means that one should give the results of all activities in performance of actions with personal desire (kamya karma) or obligatory actions (nitya karma), rather than to give up those activities completely.
For the srutis also promise results for the obligatory actions (nitya karma).
By the obligatory actions one goes to pitr loka. Brhad Aranyaka Upanisad 1.5
dharmena papam apanudati
By following dharma, one eradicates sin. Mahanarayana Upanisad 15.7
Therefore, in tyaga, one should perform all kamya and nitya karmas without seeking results, whereas in sannyasa one performs only obligatory duties (nitya karma) without the desire for results, and completely rejects rituals for personal gratification (kamya karma). This is the distinction of the two words sannyasa and tyaga.