A pump can lift water to a height of 33.9 feet although 22 feet is the more practical height for a pump to lift water through suction.
Pumps that push water can push water over 500 feet or more with enough horsepower.
A pump can pull water 33.9 feet horizontally using suction although a practical limit for a vacuum based water pump is around 22 feet.
A pump can push water much further than it can pull it up through suction.
An example is that a submersible pump of 1 HP can push water horizontally for as far as 100 feet to 300 feet and the higher the horsepower the further the pump can push the water.
Also the friction that is within the pipe is also the main factor in limiting the horizontal distance of the water traveling as it creates a pressure drop which hinders the flow of the water through the pipe.
Water can technically only go up 34 feet at sea level when using suction.
The reason why water can only go up 34 feet at sea level through suction is due to the atmospheric pressure.
Although a perfect vacuum could lift water to this height theoretically, the reality is that a vacuum is not perfect and the boiling point of the water is affected, and limits the actual lift of the water.
Water can go up further than 34 feet if pushed through pressure and not suction.
For example a pump could pump water further than 34 feet using pressure such as with a submersible well pump.
Submersible well pumps can push water up higher than 34 feet and with a large enough pump it can pump water 300 feet to 400 feet and more with a big enough well pump.
But with just suction, the limit to lift water is only 34 feet.
When you create suction, such as with a pump or a straw, you're also lowering the pressure above the water, allowing the atmospheric pressure to push the water up into the space where the pressure is lower.
As the pressure above the water is reduced, the water's boiling point is also lowered.
If the pressure happens to drop too low, the water will boil at room temperature, preventing it from being lifted up further.
And atmospheric pressure at sea level is strong enough to support a column of water that is roughly 33.9 feet high.