The differences between these two are much more important than the similarities. In fact, it is often said that political parties and interest groups are in competition with one another for power.
There are some similarities between these two. The main one is that they both want to get the government to do certain things. The NRA and the Republican Party, for example, both want the government to do less in the way of regulating people’s right to bear arms.
However, this is where the similarity ends. The major difference between the two is that the political parties care about many issues while interest groups only care about one. Using our previous example, it might be in the Republican Party’s interest to downplay issues of gun rights. The party might be able to attract broader support if it did not seem so dogmatic on this issue. By contrast, the NRA cares only about gun rights. It does not particularly care if the Republican Party expands its base just as long as only pro-gun people are elected to Congress.
Political parties try to create and hold together broad coalitions. They want to be able to govern effectively over a range of issues. Interest groups do not care about broad coalitions. They only care about winning on their particular issue.
(Hope you like my answer!) •^•