Bowls . Indoors this is played on carpet.
Outdoors it is played on grass, either Flat Green or Crown Green.
There aren't many professional players of Bowls, in any of the three disciplines, but they do exist.
The distance that the bowl has to travel is the same on both carpet and grass.
Of course it takes a lot more effort to send the bowl on grass, making the two disciplines very different to play.
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The closest examples I can think of to tennis, where the same rules apply across significantly different surfaces are soccer, American football and baseball, all of which can be played on both natural and artificial turf.
Taking a slightly wider definition of "one sport", there are some more examples: Athletics events happen on the track and on the open road (marathons).
Professional cycling happens both in velodromes and on the open road.
Canoeing/kayaking happens on both flat and downhill courses.
Equestrian events happen both in the arena (dressage/show jumping) and outside (cross-country).
Volleyball happens both indoors and on sand.
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Athletics (track and field) is contested across several surfaces.
The "road" disciplines are contested on city streets (concrete, tarmac, etc.) and cross-country is in parks (grass, rocks, trails, etc.), but those could be argued to be different from track and field.
Within specific disciplines, several events are contested on different surfaces.
Most notably, track events may be contested on 400m unbanked outdoor tracks and 200m banked (or unbanked) indoor tracks, even though the actual track surface may be the same indoors and out.
The shot put uses different equipment indoor and out because the shot is put into a sector marked in sand or grass outdoors, but is usually landing on a hard (or lightly padded) floor indoors.
The characteristics of the runways used for the pole vault, triple jump and long jump can vary significantly from indoors to outdoors.
Leaving aside the indoor/outdoor distinction, while all-weather synthetic surfaces are now the norm in athletics, until Mexico City in 1968 the Olympic track events were still contested on packed "cinder" tracks (with interesting results in Tokyo, where rainy weather made the inside lane of the track soft and uneven late in the distance races).
Also, some grass tracks are still maintained, although not often used for competition these days.
The rules of the sport allow for all of these surfaces.
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Just another sport apart from the ones Philip Kendall mentioned, is cricket.
While the outfield has to be of grass, the pitch can be of varied types.
The condition of the pitch can vary from a green top to a completely dry,dusty surface.
Like tennis, the different conditions of the pitches will suit different players/teams.
The various types of pitches include: (non-exhaustive) Green top (significant grass cover)
Hard (bouncy surfaces)
Dry (dry grass cover) Dusty (dry without any grass cover)
Sticky (comparatively wet, generally due to rainy weather)
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Rugby union is now played at the national and international level on grass and also 3G artificial pitches.
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SQUASH is an example.
there are several playing surfaces: wood concrete plaster rubber panel(rare)
glass(rare)
More details can be found here .
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Other than tennis, which sports, at a professional level, are played on  intentionally  different surfaces?
What sports at a professional level are played on multiple surfaces?
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Bowls, cycling and equestrian events are all practiced on different surfaces. Some forms of athletics are also practiced over more than one kind of surface, e.g. the marathon and cross-country running. In addition, some sports like cricket and rugby can be played on both real grass and artificial turk. There is a great number of professional level sports played on multiple surfaces. These include bowls, America football and baseball, cycling, canoeing/kayaking, riding, cricket, rugby and squash. These sports are played in two or more surfaces, while different rules may apply. Special attention should be paid to athletics, which can take place on different tracks, on fields, but also on open roads.
There is a great number of professional level sports played on multiple surfaces. These include bowls, America football and baseball, cycling, canoeing/kayaking, riding, cricket, rugby and squash. These sports are played in two or more surfaces, while different rules may apply. Special attention should be paid to athletics, which can take place on different tracks, on fields, but also on open roads.