Interest groups and political parties are very different entities. An interest group focuses money, donations and efforts towards achieving a specific policy that achieves its goals or benefits its backers. For example, the National Rifle Association is an interest group that wants to limit gun control laws, and to that end influences policy by making campaign donations towards pro-gun rights political candidates. They also employ full time lobbyists on Capitol Hill and a team of lawyers to challenge what they view as unfair gun laws in the court system.
Political parties, by contrast, are organizations based around a broad philosophy that concentrates money and ground-based operations to elect candidates of similar belief systems. In the United States, the two main political parties, Democrats and Republicans, are so large and well-funded that they essentially prohibit any third parties from entering government positions in large numbers. So their influence on policy is more indirect than interest groups, as politicians must conform to some degree to the wishes of parties in order to win financial and organizational backing in elections.