Yes, there are different ways of entering a data in a short format. The CLDR chart on Md notations illustrates the variation. Many languages use d/M notation, but d.M, M-d, and other notations are used, too. The notations used in CLDR are explained in the LDML specification; “Md” stands for month and date notation consisting of shortest possible numeric notation for month, M, and day, d, with language-dependent punctuation and order.
The M/d vs. d/M case is particularly problematic, because both notations are used in English, as well as in other languages.
Data consisting of two numbers separated by a slash should be accepted on input only if you can be sure to know which of the two different notations M/d and d/M is meant. When can you be sure of such things? Just giving people instructions doesn’t guarantee anything. Calendar widgets for input have their problems, but at least they avoid the confusion between 4/7 and 7/4.