A filter works by removing particles and microbes from water, whereas a "purifier" uses various methods to disinfect it, like UV light or MIOX®, or even a combination system like the MSR Sweetwater® purifier.
For a device to be labeled as a purifier, it needs to meet the EPA Guide Standard for Testing Microbiological Purifiers, which means it has to inactivate all three types of microbes: protozoa, bacteria, and viruses. Generally, filters claim to remove only protozoa and bacteria, which is usually sufficient for most travel in developed countries. Some filters can also act as purifiers, but they often have very small pore sizes that can lead to quick clogging. In short, being classified as a "purifier" means the device must effectively inactivate viruses, along with protozoa and bacteria.