Isaac Newton theorized and it is now commonly taught and believed that Earth's ocean tides are caused by gravitational lunar attraction. The Moon's gravity allegedly generates something called "tidal force" which causes Earth and its water to bulge out, not only on the side closest to the Moon, but also the side farthest from the Moon. Using their own calculations and predictions, however, if the Moon is only 2,160 miles in diameter and the Earth 8,000 miles, it follows that Earth is 87 times more massive and therefore the larger object should attract the smaller to it, and not the other way around. Heliocentrists claim Earth's greater gravity is what keeps the Moon in orbit, therefore it is impossible for the Moon's far lesser gravity to supersede the Earth's gravity at Earth's sea-level, where its gravitational attraction would even further out-trump the Moon's. If the Moon has enough attractive influence to lift the ocean's water even a single inch from their deep recesses where Earth's gravitational attraction is exponentially greater, then there is nothing in the theory of gravity to prevent the water from continuing its attraction all the way to the Moon. Furthermore, the velocity and path of the Moon are uniform and thereby should exert a uniform influence on Earth's tides, when in actuality the Earth's tides vary greatly. At Port Natal, for example, the rise and fall is only 6 feet, while at Beira 600 miles up the coast, the rise and fall is 26 feet. Not only this, but if the Moon's gravity was truly generating a tidal force causing Earth and its water to bulge out, then all the world's lakes, marshes, ponds and other inland waters would be similarly affected and have tides as well. These and other problems caused Isaac Newton to openly admit that his explanation of the tides was the "least satisfactory" portion of his theory of gravitation...
Because of inverse square law the amount of gravitational pull by the moon and sun felt on earth is puny compared to how much we feel from the planet itself. However when you take into account it’s force acting on a fluid ( the oceans), especially a vast quantity of fluid with a complex boundary, and that force acting unequally but periodically over time, that force than creates conditions for wave formation. And that is what tides are. It is a global oceanic wave induced by the gravitational influence of the sun and moon. It is NOT the water pulling up into the sky because of the moon. Their gravity felt from earth is too small for that. However it is enough to disturb a relatively frictionless fluid and form a wave. This is also why the tide times are highly correlated to moon position.
This is why tide is high on opposite sides of the world at the same time, tides are a sine curve ( a wave) and half of the earth is 180 degrees out of phase from the other ( corresponds perfectly with the gravitational influence of moon). This also explains why the tides rise and fall in a sinusoidal and not linear rate ( sometimes complicated by shoreline geography)
As to why some areas that are relatively close can have large variance of tidal range is simple. Shoreline geography. All of the areas that have large tides have something in common- they are at the head of or alongside gulfs, bays or fjords. Areas of small tides are alongside wide open coasts. Look at the map of the areas you cited as examples. Port Natal is on a wide open coast. Further north you will find bierra situated at the head of a large bay. Why does this matter? Because as the tide (wave) approaches shore and there is a constriction of some sort the wave form gets compressed and the amplitude increases. Also the Venturi effect amplifies this as well. Look up the Bay of Fundy to see an extreme example ( largest tide in world) and the tides on the Atlantic coast of Florida for the other extreme ( very small tides).
Celestial objects and gravity also explain the spring and neap tide phenomenon ie why tides are highest during the new moon and full moon and smallest during half moon phases. Because gravity is a vector quantity it’s overall force of influence takes direction into account. So when the sun and moon are lined up ( full or new moons) the exert a higher overall force exacerbating the wave. And during half moons they are at a 90 degree relative to earth so their pull is spread out and tides are smaller. You can see it with your own eyes over the course of a month and it is a globally synchronized phenomenon.
I am a sea captain, sailor, and sea kayaker who has been on many oceans and coasts. I have seen the standard model play out before my very eyes. Why else would moon phase have anything to go with tidal range globally? Why else does shoreline shape dictate tidal range locally? Tide charts and tables are accurate to an incredible degree of precision, and are all based entirely on Newtonian physics and the relative position of sun and moon. I have staked my life on the accuracy of these models and like clockwork they are right. How could this otherwise be?
Newton may not have fully understood, but his math ( calculus) and models ( basic gravitational theory) have given us a very strong model for not only how tides work, but how to predict them to a very high degree of accuracy. The earth is a sphere. It orbits the Sun. The moon orbits the earth. If you have any questions please ask them.