What is the difference between a step-up and a step-down ring?
I want to put a large diameter filter on a small diameter lens.
Do I need a step-up ring or a step-down one?
A step-up ring allows you to fit a filter that has threads larger than your lens. A step-down ring does the opposite (with possible vignetting issues).
If you have 72mm lens threads and want to fit a 77mm filter, you need a step-up ring. If you have 77mm lens threads and want to fit a 72mm filter, you need a step-down ring.
So in your case you want a step-up ring.
Adaptor rings that are threaded on both sides come in three versions. Male to Male thread, Female to Female thread, and Male to Female thread. The MtoF are often called step up/ step down rings. Looking at some I have from K&F and Rise(UK) They both follow the same pattern. The first number is Male and the second number is Female.
So a 52mm-49mm ring and a 49mm-52mm ring would have the first number be male, a 52mm male and a 49mm male followed by the 49mm female and 52mm female.
If the lens had 49mm filter threads a larger filter could be used with an adaptor. Thinking that 49mm male thread would fit to the lens then a 49mm-52mm or a 49mm-55mm would allow use of 52mm or 55mm filters.
Male to Male thread work to reverse mount one lens to another lens for closeup and macro photos. If the 200mm lens had 52mm filter threads and the 50mm lens had 49mm filter thread a MtoM 52mm-49mm would join them. Which would be close to 4X. Divide the long lens by the short lens to get enlargement factor. These adaptors would work to mount a reversed lens to an adaptor that has female thread and the male lens mount.
I have not noticed if the adaptor would be labeled 52mm-49mm or 49mm-52mm. On Amazon I have only found one maker that has lots of M/M options and they are all listed single rather than a list to choose from so it is a pain to find them. They have big yellow numbers on the listing web page. Lots of scrolling through the pages.
Rise(UK) have odd sizes like 30.5 and 40.5 that fit enlarger lens for use on bellows. So the enlarger lens have male thread and the adaptor would have the second number be the female to fit it. 52mm-30.5 49mm-30.5 then could fit to a female thread to camera male mount adaptor. Or if your camera adaptor had male thread to Male camera then a Female to Female adaptor would join them all together.
The 'step' terminology is from the lens's POV.
So, going from a smaller lens to a larger filter is a step-up ring.
Going from a larger lens to a smaller filter is a step-down ring.
Most folks would not recommend using a step-down ring because vignetting is a possibility.
It's usually best to find a "standard" size of filter that's as larger or larger than the filter threads on most if not all of your lenses [e.g., 77mm], so you only have to buy a single set of filters and step-up rings to use them on all your lenses.
Let me make this clear there is no such thing as a ring that allows you to fit a smaller filter on your lens.
Step up rings are standard rings that step incrementally so you have to stack them until you get the desired Diameter.
Step down rings are if you are lets say using a HOYA 77mm Variable ND Filter and want to adapt it to multiple lenses. you would use a single stepping ring to go down to the number you desire ie. 77mm to 59mm