"equity" has many meanings. The one which is perhaps most similar to that of "equality" is "fairness".
"Equality" relates to treating people equally. It is possible to treat two people equitably (fairly) but not equally.
For example, if I injure a doctor and a cleaner with my car and both are unable to work for one week, I will have to pay one week's loss of earnings to both people. Some people would say that this law is equitable - there is "equity". However, I will pay more to the doctor because he earns more and so the compensation is not "equal" - the system lacks "equality".