Moore says he was fined $7,500 by the NFL for a hit in last week's loss to Tampa Bay, while Taylor was docked for a hit on Miami quarterback Chad Henne.
There was some confusion when Moore said Wednesday he was fined for a helmet-to-helmet hit that did not draw a penalty.
Instead, coach Mike Smith confirmed the fine was for an unnecessary roughness penalty when Moore used his helmet to hit running back Earnest Graham in the third quarter of the Buccaneers' 16-13 win.
Moore had four tackles and an interception in the loss.
It is the second straight week the league has fined an Atlanta defensive back. Cornerback Dunta Robinson was fined $40,000 for leading with his helmet on his hit on Philadelphia receiver Jeremy Maclin on Sept. 18.
Taylor was notified Wednesday by the league of the penalty, assessed for hitting a sliding Henne in the fourth quarter of Cleveland's 17-16 win. Henne scrambled for six yards and hit the ground before he was struck by Taylor, who received a 15-yard personal foul for unnecessary roughness.
Taylor will appeal the fine.
The Browns drafted Taylor with the No. 21 overall pick in this year's draft. Through three games, he has 18 tackles and one sack.
Information from The Associated Press contributed to this report.