The behavior of the @JvmStatic annotation is explained in detail in the documentation. When reading the documentation, you should assume that it gives you all the important information, and behavior differences that are not mentioned in the documentation do not exist.
In this case, the documentation says:
If you use this annotation, the compiler will generate both a static method in the enclosing class of the object and an instance method in the object itself.
In other words, the effect of the annotation is that it tells the compiler to generate an additional method.
Does the documentation mention that there is any difference in behavior or memory allocation? It does not. Therefore, it’s safe to assume that there is none.
Is there a preference on which one to use? Normally, an API is declared in one place and used from multiple places. If you’re calling a method from Java, then you should declare it as @JvmStatic, because adding the @JvmStatic annotation in one place will allow you to leave out multiple .Companion references in multiple places.
Do both create a pseudo static singleton object, like Java static does? This question does not make sense, because Java static does not create a “pseudo static singleton object”. If you declare a static method in a Java class, and then call this method, no objects will be created.