What is a profound difference between how and why?

The most profound difference between ‘how’ and ‘why’ that I can think of is a difference which relates to the aspect of the solution that is being brought into focus. To make this clearer, allow me to employ a series of examples;

Why did the ball fall to the ground? vs. How did the ball fall to the ground?

Why can the coin only land on heads or tails? vs. How does the coin only land on heads or tails?

Why does the world exist? vs. How does the world exist?

This distinction I intend to illustrate by analogy.

(WHY:) The reason that the ball fell to the ground is that the ball was very close to the surface of the Earth and at this distance, (the cause =) Earth’s gravity is strong enough to pull other objects towards it. vs. (HOW: the deterministic specification =) The distance between the two objects corresponds to a potential energy at rest of X which, when released, is immediately expended through the act of moving towards the Earth as gravity is acting upon the object at all times while it is within a certain specified range of the Earth.

(WHY:) The reason that the coin can only land heads or tails (discounting the outlier case of an edge landing for the purposes of this example) is (the cause =) because there are no other options; the law of the excluded middle and the law of non-contradiction impose the valid dichotomy of heads or tails and, when the coin is thus flipped, at least and only one of the proposed outcomes is a necessary result - 1/2 possible end states must be realized, wherein both (0/2) and (2/2) are logically impossible. vs. (HOW: the deterministic specification =) The shape of the coin, with its dual and opposite faces, allow the physical influences of the environment to affect the coin in a very specific and finite set of ways; this means that as the coin is flipped in practice, it is exposed to a whole variety of physical factors which an adequately precise simulation could incorporate in order to infallibly predict the outcome, as the resulting effect is a deterministic consequence of the variables involved and the principles of physics, which govern the behaviour of the coin when it is flipped.

(WHY:) The world exists because such a truth is fundamentally and logically necessary according to (the cause =) the principle of sufficient reason, for to suppose otherwise is a demonstrable contradiction which is thus logically impossible. vs. (HOW: the deterministic specification =) The world exists due to the inherent natural form of the fundamental ontological elements; the world as we know it is a non-contingent consequence of the basis of Being, wherein the spatiotemporal environment within which we find ourselves is naturally entailed by the foundation of existence.

In the above responses to my conjectured queries, we can see that although each response contains similar information, the why and the how are nonetheless speaking to slightly different points: Why describes the sufficient reason that a specified observed state of affairs is the way it is and happens the way it does - it must because X principle is true and contextually relevant. How, on the other hand, deals with the specific description of the form that necessity takes, dealing instead with the principles and variables which so made it necessary for this specified outcome to occur rather than any other logical possibility - this is the only ‘outcome’ we have access to because these - Y - are the specs of this universe.

As might become clear upon an examination of the set of examples I have provided above, as I vary the analytical scope of the questions and elevate them to more profound and generalized inquiries, the distinction between ‘why’ and ‘how’ begins to fade, almost to the level of imperceptibility.

This, of course, is what is responsible for the spectacular variety in both content and confidence displayed in response to the question I posed, as the framing of the issue which is utilized in the posted question enables the variance which is necessary to discern the subtle difference between two types of knowledge about a subject which are almost, but not quite, the same.

I hope my above exposition was as insightful as I hoped, and not as confusing as I fear. Thanks for your time!