What is the difference between data perturbation and differential privacy? I cannot distinguish the terms "data perturbation" and "differential privacy".
If the data perturbation is the process that adds some small value sampled from specific distributions such as Laplacian and Gaussian, differential privacy relies on it, right?
Is the differential privacy a just a notion for formalization of privacy?
Is data perturbation it the process used in the differential privacy?
If so, are there any other cases that use data perturbation?
Thankyou.
 A: Formal privacy, of which differential privacy is the leading example, provides a mathematical framework that quantifies the minimum amount of noise that must be injected into a statistical release in order to insure that the confidential information leakage does not exceed a stated limit, usually parameterized by epsilon. The noise injection process must be parameterized in a manner that can be proven to satisfy the conditions in the mathematical definitions of the formal privacy system. When it does, then the noise injection is formally private (differentially private, if that is the framework used). When it does not, the noise injection is ad hoc with no formal privacy properties. 
A: Differential privacy is a form of data perturbation, but it's a formal, principled approach for doing data perturbation that provides you an approach for bounding the privacy loss resulting from the publishing of your data after the perturbation.
Although you can add Laplace noise to every element of your dataset and publish a new dataset like so (this is called the "local model,") a more efficient approach is to compute the specific queries that you wish to release, and then add noise after the results are computed.  If you want to release many results, you will typically be better off using a mechanism that is further advanced, such as the Matrix Mechanism. 
A: They are different things but very united. You are right. Differential privacy is a definition (Formalization). While data perturbation is the mechanism/algorithm you use to add noise to the data in order that you could still infer something from this data without giving information from any individual from de Dataset/Database.
