Firstly, filtration is a term used to describe the removal of impurities from a desired material that can only be (in most instances) valued when it is in its most pure form. These materials can range from solids to liquids, or even gases. For example, when gold is mined, it is gotten naturally as an ore that may lack the usual gold lustre and economic value until it is filtered through a series of chemical as well as thermal processes. The end result is the isolation of the sole needed matter that is greatly soughted for around the globe.
On the other hand, boiling just implies the application of heat to liguids to a temperature that is enough to make each molecule of the fluid gain energy to escape its confinement in form of vapour. The essence of boiling is very wide as it can be used for aseptic purposes in the medical field, in households to make water free from living microns, in distillation to separate different fluids with different boiling points, and so on. In all its ramifications, heat energy must be applied to a known fluid for boiling to take place.