Step Down Ring: A filter size adapter ring that permits a lens to use filters smaller than the lens filter size. Step Up Ring: A filter size adapter ring that permits a lens to use filters larger than the lens filter size.
Step up and step down rings can bridge any gap, but you are inviting vignetting and other image quality problems if the diameters differ.
You mention the cost of filters. I purchased the filters that fit my biggest lens and then step down rings to fit the smaller lenses. I've seen people carry 2-3 various sized filters and it didn't make sense to me.
See also: Focal, Filter, Exposure, Image, Lens
 
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