What copyright reaches in an app
Source code and object code are protected as literary works, and graphics, icons, sound, written content, and audiovisual elements can be protected too. Copyright does not protect the underlying idea, the general concept, or functional features as such, so a competitor can usually build an app that does the same thing in its own way. The closer question involves user interfaces: original visual expression can be protected, but layouts dictated by function or by common conventions often are not. Patents and trademarks protect different aspects, and many app disputes involve more than one of them. Names and icons that identify the app to users may also qualify for trademark protection.
Ownership and third-party code
Apps are often built by freelancers, agencies, or offshore developers. In most of those arrangements the developer owns the code unless a signed written assignment transfers it, because work made for hire covers commissioned work only in narrow statutory categories. Check your development agreements before relying on ownership. Open-source components come with license conditions, and some licenses impose obligations to share source code in certain circumstances, so a code inventory is useful before enforcement or a sale. Libraries and assets bought from marketplaces carry their own license terms.
Responding to a copycat
App stores have complaint processes for intellectual property claims, and a notice that identifies the copied material specifically tends to be handled more effectively than a general complaint. A copyright registration is generally required before suing over a US work, and timely registration affects whether statutory damages and attorney's fees are available. Source code can be registered with portions redacted to protect trade secrets. Bring screenshots of both apps with dates, your code repository history, development contracts, and any registration records. A first conversation usually decides between a store complaint, a demand letter, or litigation. Store processes often allow the other developer to respond, so keep your evidence organized for a second round.