Filtered water is a quicker, cheaper substitute for distilled water. The two types are similar but they aren’t identical. When you filter water, the amount of contaminants that are removed depends on the type of filter you use.
Distilled water is the purest water you can create. As the water is evaporated and then condensed back into liquid form, any contaminants will be left behind. In a sense, filtration removes contaminants from water, whereas distillation removes water from contaminants.