What is the relationship between "distributive justice" and equity? Are these two ideas synonyms?
▻ DISTRIBUTIVE JUSTICE ('DJ')
DJ occurs in the allocation of rewards, resources, rights, obligations, costs and burdens - any benefit or disbenefit that has to be allocated to a number of people. If I slice a cake at a children's party, I divide the cake into equal portions : each child gets the same amount because I do not favour any particular child. In fixing salaries I might allocate payment on the basis of 'to each according to their work', 'to each according to their needs', 'to each the same' or some such formula or principle. In making redundancies - a disbenefit - I might 'let people go' on the basis that the newest staff are the first to lose their jobs.
Equity applies not in the field of distribution of benefits or disbenefits (as above). It is mainly about fair exchange - the mutually beneficial transfer of valued resources. In any situation there is usually an input/ output ratio that is fair or would widely be judged to be fair. It is hard to fix or define this ratio in advance but, for instance, if your input was 12 hours' hard work in cleaning my house, and my output was a payment to you of $1 or £2 or €3, the ratio does not seem proper or right. My output (payment) is disproportionately low in relation to your input : there is an inequitable ratio.
▻ CONVERGENT USAGE
There are other uses or meanings of equity by which equity and DJ come out the same : some might say that if I pay different salaries to two groups of workers doing identical work in two different factories, this is inequitable. This reduces equity to a form of DJ : if this situation is inequitable it is because I am not paying to each according to their work.
The account given of equity at the start marks out different work for the terms 'equity' and 'DJ'. We need both concepts, not the reduction of equity to DJ.