The smallest daily tidal range occurs during which type of tide?
We have varying differences between high and low tides because two different bodies create tides -- the Moon and the Sun.
Think of the Moon acting alone. Its gravity, or more accurately the changes in the Moon's gravity with distance across the body of the Earth, causes two high tides. One is directly aligned between the center of the Earth and the Moon, the other is on the opposite side of the Earth. In between, at 90 degrees from Earth-Moon alignment, we have low tides.
Now consider the Sun. It, too, has gravity that varies across the face of the Earth. The total amount of gravity the Sun exerts is more than what the Moon exerts, but solar gravity varies less across the body of the Earth so the Sun contributes less to our tides than the Moon. Still we have solar high tides in the line from the Sun through the Earth, and solar low tides 90 degrees out of line.
Now put the Sun and the Moon together. If the two bodies are in the same line with the Earth, at full and new moons, then the high tides are raised by the Sun and Moon at the same time and place to make especially high tides. Correspondingly the low tides at the 90-degree positions are especially low. This is called spring tide.
On the other hand, when we have quarter-moons -- the Sun is at 90 degrees from the Moon when we look ftom Earth -- the tides oppose each other; the Sun would make high tides where the Moon wound make low tides and vice versa. The Moon wins out because we saw that it makes stronger tides than the Sun, but the difference is typically half of that in spring tides, or less. We call this neap tide.