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Sankhara is a very broad word with many meanings or contexts (see link). For example, 'sankhara' can mean 'condition thing' therefore a material thing such as a tree or rock can be a 'sankhara'.
In the context of 'sankhara' a mental processes, unusually, the Parivatta Sutta states the sankhara khandha (aggregate) is intention. Since AN 6.63 states: "kamma is intention", it may seem 'kamma is sankhara' but this is not really ideal because it creates confusion. This is because a Buddha or arahant still has a functioning & pure sankhara khandha (aggregate) despite a Buddha has eradicated kamma (in the ordinary sense of the word).
Therefore, it is best to not regard 'sankhara' & 'kamma' as synonyms.
As a mental process, sankhara is 'thought'. There can be pure & undefiled thoughts. However, kamma is generally always impure & defiled, including 'good' karma (refer to MN 117).
There is pure kamma (per AN 6.63) however this pure kamma is the kamma that ends kamma. Because this type of kamma destroys kamma, it is best to not call it 'kamma' since how can the ending of kamma be kamma?
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They are not synonyms. Kamma is one entity of Sankharas Dhamma. We can be taught by the following Buddha saying.
Intention (cetana) I tell you, is kamma. Intending, one does kamma by way of body, speech, & intellect.
Cetana is one of the Nama Kaya and as well as Sankhara Dhamma. Collectively speaking, everything is Sankhara Dhamma except Nirvana. Only Nirvana is Asankhara Dhamma (it is not maintained, use no effort to persist, not needed continuous care to survive/last).
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I am also trying hard to understand the difference. however no one is giving satisfactory answer. so I have to discriminate based on my own gut feeling. So I am trying to explain by taking a case of killing someone.
List of pali quotes
cetanāhaṁ, bhikkhave, kammaṁ vadāmi. AN 6.63 (Note :cetnā =kamma)
ceteyyaṃ abhisaṅkhareyyaṃ DN9 (dont execute, dont develop)
Cetayitalakkhaṇā, mahārāja, cetanā abhisaṅkharaṇalakkhaṇā cā”ti.(Abhisankhara is characteristic of Cetana, this is deadlock)
akusalaṃ kammaṃ cetanāya cetayitvā (Note : Cetnā is execution of kamma)
evaṁ anassāsikā, bhikkhave, saṅkhārā”, “Bhikkhus, you should not cultivate saṅkhārā.(Note : sankhara are to be developed)
rūpasañcetanā, saddasañcetanā, gandhasañcetanā, rasasañcetanā, phoṭṭhabbasañcetanā, dhammasañcetanā. these are 6 types of sankhara SN 22.6 (sañcetanā= sankhara , here is deadlock. but I guess cetanā is more complex then sañcetanā So we can give benefit of doubt)
Kāyasañcetanā kāya saṅkhāro, vacīsañcetanā vacī saṅkhāro, manosañcetanā citta saṅkhāro ( again sañcetanā = sankhara)
Saṅkhatam-abhisaṅkharontīti kho, bhikkhave, tasmā ‘saṅkhārā’ti vuccati. Rūpaṃ rūpattāya saṅkhatamabhisaṅkharonti, SN 22.79( Sankhara(Actor) Acts(Abhisankharoti), on SAnkhata(the conditioned)
and most popular
Conclusion
saṅkhāra and kamma are not same.They have different lifecycles. and they meet at point of execution. Kamma is dependent on saṅkhāra. but saṅkhāra is not dependent on kamma. saṅkhāra can strengthen or weaken without kamma. but kamma always strengthens saṅkhāra.
Explanation with example
When you kill some one that is action. kamma. and you did lot of planning and preparation to kill one. that is saṅkhāra.
The result of kamma is punishment/reward. whereas result of saṅkhāra is mastery/ addiction.
First time when you kill someone you need lot of mental work , to plan and prepare yourself to kill. you need to resolve lot of internal conflict, shame, fear etc... but this effort reduced by half when you kill second time. and later on killing is so natural for you that you can kill someone just like one kill a mosquito. that is because you have generated saṅkhāra of killing.
Lets say you killed 5 people(ceteyyaṃ abhisaṅkhareyyaṃ). this means your killig saṅkhāra is 5 time stronger(abhisaṅkhareyyaṃ). but you have 5 kamma seeds (ceteyyaṃ)waiting for you to be killed by someone in future. now these are separate entities.
saṅkhāra stays with you, as your personality. and thats why it is part of panca-upadan Khanda. whereas Kamma seeds are not part of you. its not your identity. its out there in universe(or deep down ) waiting for appropriate time to come as kamma vipaka.
When you learn driving, the art of driving is part of your saṅkhāra Khanda, but it can not create any good/bad kamma-vipaka on its own.
As child our personality is build by parents, teachers and friends. We see our parent fighting, drinking etc.. This builds saṅkhāra in us. however there is no kamma. As adult your personality is replica of all that you accumulated as child. but you are unable to generate strong kamma seed with that saṅkhāra during your childhood. If a child kills someone, court also can not punish him strongly.
As an adult you wish to kill someone, but you very well know you can not kill, and you are not seriously planning to kill. so this is weak saṅkhāra but that does not mean there is no kamma. you have done weak kamma also. which will bring vipaka later.