Both remedies can compel action, but they arise from different legal traditions with different requirements.
Mandamus and injunctions can sometimes achieve similar practical results — an order requiring someone to do something — but they come from different legal traditions and require different showings.
The equitable roots of injunctions
Injunctions arise from equity practice and are available in a much broader range of disputes, including between private parties, not just against government officials performing public duties. A mandatory injunction, specifically, orders a party to take an affirmative action, functioning similarly to mandamus in that narrow respect.
Different tests, different emphasis
Injunctions generally require a showing of likelihood of success on the merits, irreparable harm, a balance of hardships favoring the requesting party, and consistency with the public interest — a four-factor test quite different from the three-part mandamus standard focused on clear duty and clear right.
Availability against private parties
One of the most important practical differences: injunctions are widely available in private civil disputes (for example, between two businesses), while mandamus traditionally applies to public officials and entities performing public duties, with only limited exceptions for private entities exercising a public function.
Overlap in government litigation
In cases against government defendants, plaintiffs sometimes plead both mandamus and injunctive relief claims in the same case, particularly in APA litigation, since courts can grant relief under whichever theory best fits the facts without requiring the plaintiff to choose exclusively between them at the outset.
Practical guidance
If the dispute is between private parties, an injunction — not mandamus — is almost certainly the relevant tool. If the dispute involves a government official's failure to perform a legal duty, mandamus (potentially alongside an APA claim) is usually the more precisely fitting remedy.