There is a lot of overlap between trails and linear parks, but they are not synonymous. Trails that are not designed for recreation wouldn’t necessarily be considered linear parks, and linear parks that do not serve a transportation purpose wouldn’t necessarily be considered trails. However, in many cases they will be the same thing, because a trail that is fun to use is going to get more use, and a linear park that can get you from point A to point B will get more traffic, so incorporating elements of both is a recipe for success.
My favorite linear park is the Bridge of Flowers in Shelbourne Falls, Massachusetts. I had the opportunity to visit last year, and not only was it stunning, it was an innovative use of a decommissioned trolley line. Building from the shape of the trolley line, it is inherently linear, and the gorgeous landscaping with places to sit at either end make it clear it is a space you are meant to leisure in. https://www.bridgeofflowersmass.org/
The Rose Kennedy Greenway in Boston is another excellent Massachusetts linear park. Winding through downtown Boston, covering the formerly elevated highway, it is a pedestrian-friendly route through the city, but it also had ample recreation programming and spaces to spend time. https://www.rosekennedygreenway.org/
The High Line in New York is perhaps the most famous linear park in the United States. A popular tourist destination, it draws crowds for the sole purpose of leisure in the space, but like the Bridge of Flowers, it’s place atop an old rail line makes it inherently linear. https://www.thehighline.org/