Are all filters purifiers?

A filter is a "purifier" if it is capable of inactivating viruses, protozoa, bacteria, algae, and fungi, . Not all filters can do that. Some gravity water filters are good at that.

Emergency water purification methods:
boiling the water and straining it through a cloth
adding 3 drops of tincture (alcoholic solution) of iodine per each quart of the water
adding 10 drops of 1% chlorine bleach per each quart of water.

Thoroughly mix with the water, and let to stand for 30 minutes.

Strain through cloth to remove particulate matter.