Here's a breakdown of the situation:

* The Sun's Gravity: The Sun is much more massive than the Moon, and its gravitational pull on the Earth is significantly stronger. However, because the Sun is much further away, the difference in its gravitational force across the diameter of the Earth is relatively small.

* The Moon's Gravity: The Moon, despite being much smaller than the Sun, is much closer to the Earth. This means the difference in its gravitational pull across the Earth's diameter is much more pronounced.

The combined effect of these forces is responsible for tides:

* High Tides: When the Moon is directly overhead or on the opposite side of the Earth, its gravitational pull is strongest. This pulls water towards the Moon, creating a bulge on the side facing the Moon and a corresponding bulge on the opposite side. These bulges represent high tides.

* Low Tides: As the Earth rotates, areas that were experiencing high tides move away from the Moon's strongest gravitational pull. The water in these areas flows back, leading to lower water levels – low tides.

Important Notes:

* The Sun's gravity also plays a role in tides, but its effect is less pronounced due to its distance. When the Sun, Earth, and Moon are aligned (during a new moon or full moon), their combined gravitational pull creates stronger tides – spring tides.

* When the Sun, Earth, and Moon form a right angle (during a quarter moon), their gravitational pulls partially cancel each other out, resulting in weaker tides – neap tides.

In summary, the Sun and Moon's gravity do pull on the Earth's surface in opposite directions, but the difference in their gravitational forces is significant enough to cause tides. The Moon's gravitational pull is the primary factor, while the Sun's gravity contributes to the overall tidal phenomenon.