I don't think the distinction is in what's under foot merely that it is a path or trail around the city of Brussels taking in non-built areas

park/forest trail, as opposed to roads

See description of a 'green walk' in London:
http://www.tfl.gov.uk/streets/walking/walkdetails.asp?id=39

First off I think you'll have to identify what this "promenade verte" is exactly, since there are variants on a theme. Here are some ideas from my notes:

Allée verte Greenway, green corridor, green chain. Cf Trouée verte.

Trouée verte Discrete green space (small scattered, dispersed areas, not interlinked, not greenways)

Whether this "promenade" is simply Belgian for what I (and others - I think you'll find entries on ProZ for "allée verte") have encountered as "allée" or something different, I cannot say. At first sight though, it looks as if it might be a "greenway":

Aiming to connect all the major cities of the East Coast along a continuous, off-road path, the East Coast Greenway spans 2,950 miles from Calais, Maine to Key West, Florida. With the trail now 21 percent open for public use, individuals and communities all along the East Coast are already beginning to enjoy the Greenway's many health and economic benefits
http://www.greenway.org/

greenway (greenways). A corridor of vegetated space (e.g. a boulevard planted with trees and flowers) in a planned city or town ...
www.informedesign.umn.edu/Glossary.aspx?id=1905

Greenway: A greenway is a corridor of open land that provides one or more of the following benefits: (1) protection and management of natural and cultural resources; (2) provision of recreational opportunities; and (3) enhancement of the quality of life and the aesthetic appeal of neighborhoods and communities.
http://www.raingardennetwork.com/glossary.htm

Greenway: A network of protected open space buffering waterways, linking larger natural preserves, and protecting ...
www.drgreenway.org/glossary.html

Greenway
– A greenway is a corridor of open space. Greenways vary greatly in scale, from narrow ribbons of green that run through urban, suburban, and rural areas to wider corridors that incorporate diverse natural, cultural, and scenic features. They can incorporate both public and private property, and can be land or water based. They may follow old railways, canals, or ridgetops, or they may follow stream corridors, shorelines, or wetlands, and include water trails for non-motorized craft. Some greenways are recreational corridors or scenic byways that may accommodate motorized and non-motorized vehicles. Others function almost exclusively for environmental protection and are not designed for human passage. Greenways differ in their location and function, but overall, a greenway will protect natural, cultural, and scenic resources, provide recreational benefits, enhance natural beauty and quality of life in neighborhoods and communities, and stimulate economic development opportunities
www.brodheadwatershed.org/bwa/PDFplan/glossary.pdf


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Note added at 2 hrs (2006-12-05 01:26:57 GMT)
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About the East Coast Greenway

The East Coast Greenway spans the eastern seaboard from Calais, Maine to beautiful Key West, Fla. Pictured here is the Greenway's southern gateway marker, set in St. Croix granite from the Calais area.Walkers, cyclists, and other trail advocates have joined forces around an audacious project, a 2,950 mile TRAFFIC-FREE path linking East Coast cities from Maine to Florida. Launched 14 years ago, this vision for an urban alternative to the highly popular Appalachian Trail is now 21% built as an OFF-ROAD route. In 2006 we will unveil our continuous route, with on-road routing linking completed OFF-ROAD sections.



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Note added at 2 hrs (2006-12-05 01:50:37 GMT)
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For an ORLANDO greenway that IS a greenway:

http://gorp.away.com/gorp/location/fl/ww_orlando3.htm