Question

Simple “No” answer will calm me.
If there is any difference then what it is?

Answer 1

No

As long as the Activity or Window that calls getLayoutInflater() has the same Context that would call getSystemService(), there is no difference.

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Proof You can trace the LayoutInflater returned by getLayoutInflater() to LayoutInflater.from() and you can see this is just a shortcut for getSystemService() from the source code:

public static LayoutInflater from(Context context) {
    LayoutInflater LayoutInflater =
            (LayoutInflater) context.getSystemService(Context.LAYOUT_INFLATER_SERVICE);
    if (LayoutInflater == null) {
        throw new AssertionError("LayoutInflater not found.");
    }
    return LayoutInflater;
}