Is that the standard for an area variance or a use variance, or both? In New York, the standards are very different, with an area variance being much easier to obtain, and a use variance next to impossible.
The standards you outlined will not work if the code does not comport with what is actually on the ground. For New York, the Sasso v Osgood case is the way out of the box when that obtains.
I'm not quite sure what you NY means by the two types of variance. In IL there are text amendments to a zoning map which are hard to obtain, but I don't think that's what you mean.
The variance standards I listed above apply to things like setbacks, parking, height and signage - I think that is what you are calling an area variance. They are easy, but are presumed invalid unless the above findings are met.
There are also special (conditional) use permits which are applicable for certain defined uses in specific zoning classes. Examples could include a church in an estate residential district or a nursing home in a business district. The application is much tougher than for a minor variance, but unlike the above variance, special uses are presumed valid if the findings are properly established. Perhaps that's what constitutes a NY use variance. An example of the standards used for findings of fact for these special use cases are:
(A) Is necessary for the public convenience at that location or, in the case of existing nonconforming uses, a special use permit will make the use more compatible with its surroundings;
(B) Is so designed, located and proposed to be operated that the public health, safety and welfare will be protected;
(C) Will not cause substantial injury to the value of other property in the neighborhood in which it is to be located; and
(D) The proposed special use is designated by this code as a listed special use in the zoning district in which the property in question is located.