Even during the 19th Century, there were at least three distinctly different types of target rifles in use in the USA. One type was indeed, the heavy, long barreled, "over-the-log" rifles (AKA "chunk-guns"), of the type smylee mentioned. These were round-ball guns, generally with fixed, open sights. Matches were generally at sixty yards, prone position.
A second type, more common in the northeast and upper Midwest, was the "yankee" target rifle, intended for bench rest shooting at long range. These were sometimes extremely heavy, rifled with gain-twist, or a uniform fast twist, and intended to shoot an elongated bullet, rather than a round ball. Matches were usually between two individuals, and at ranges of forty or eighty rods (220 or 440 yards).
The third type was the "Schuetzen" target rifle, popular in communities with German, Swiss, and Austrian heritage. These were "offhand target rifles", with very distinctive stock architecture, often with massive cheekpieces, palm-rests, elaborate trigger guards, and butt plates. Matches with these rifles were usually at 200 yards (more elongated bullet guns), and fired from a standing position.