The main similarity between political parties and interest groups is that they both seek to achieve certain policy objectives. These can be a broad range of policy objectives or only a relative few.

Political parties have a large number of policy objectives that they wish to achieve, whereas pressure groups tend to have only a few. Some pressure groups, such as those that campaign for the protection of the environment, are based around a single issue.

As such, pressure groups tend to have greater coherence than political parties, as it is much easier for their members to unite around a common single objective than a broad range of policies.

This helps to explain why pressure groups endeavor to bring about changes in policy without attaining political power. Their focus is so narrow that it would be virtually impossible for them to secure the kind of broad-based coalition that is essential in a democracy for a political party.

However, despite remaining outside of the formal democratic process, pressure groups—as their name implies—can still exert considerable pressure on policy-makers in order to get the changes that they seek.

Such changes are not always forthcoming, however, because political parties tend to be quite broad-based coalitions. This means that policy-makers need to take into consideration a broad range of stakeholders whose interests are often opposed to those of relevant pressure groups. As a consequence, any changes made by political parties in power tend not to be as bold or as radical as pressure groups, who don't have to deal with the necessary compromises of political power in a democracy, would like.

Interest groups (also known as advocacy groups or special interest groups) are defined as organized groups of individuals who come together because they share common interests and viewpoints (often political or economic) and wish to address common concerns and issues. The main goal of interest groups is to influence public opinion and policy-making and ultimately shape public policy to their benefit or in their interest; in fact, the desire to affect the government and influence the public opinion is the biggest and most notable similarity between interest groups and political parties. Both political parties and interest groups are formally organized and can vary in size.

The main difference between interest groups and political parties is that, aside from influencing public policy, political parties also wish to control and run the government. The primary focus of a political party is to win elections and gain greater political power. Interest groups can openly support and advocate for certain political candidates (which is one of the reasons why they're also called advocacy groups), but, unlike political parties, they can't offer political candidates who can compete in a country's elections.

Political parties can also be concerned with multiple different issues and policies, while interest groups focus predominantly on one main issue or area of interest.

The similarities between interest groups and political parties are broad. Both interest groups and political parties try to shape political policies. Both try to protect and promote the causes they support. Beyond that, they differ quite a bit.

An interest group is a group that shares a common interest. (That sounds pretty obvious.) These groups can be formal, informal, or both. For example, you could have a large, informal interest group made up of several formal groups, as well as unaffiliated individuals. The environmental movement is a large, diverse interest group. It contains dedicated individuals as well as quite distinct organizations. The main thing that unifies an interest group is commitment to a specific cause or interest. They might actually disagree about what form support for that cause would take. Interest groups might donate to politicians, or support specific legislation, but they are not usually a formal part of the government.

Where an interest group focuses on specific interests, political parties often represent an array of interests. Ideally, these parties are unified, but that's not always the case. Political parties share a history and an ideology.

As an example, consider the Libertarian Party. It is unified by its support of individual liberty and the free market and opposition to government action. Many different interests groups might support this, interest groups that would otherwise have little to do with one another. For example, someone who supports drug legalization (and is part of that interest group) might find him or herself beside an abortion rights activist (another interest group) in supporting the Libertarian Party (a political party).

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.