Stained glass is the older material, it is glass that has some impurities added to it when it is made to give it a given color. These filters are cheap and in some applications work well. Interference filters use very thin glass and coatings to set up constructive and destructive interference in the filter. This interference creates the filter effect. These filter can be made to just about any specification you want.
Most modern microscopes use interference filters for fluorescence.
An interference filter is usually a band pass filter. It is specified by the center wavelength and the width. Manufacturers of interference filters provide charts of the intensity versus wavelength. A chart is the best way to understand a band pass filter. A wavelength chart shows two other filter phenomenon, filter factor and filter inefficiency.