There are a whole range of identifiers for digital objects, so it can be difficult to know which is best suited to your situation. A useful place to start could be watching this webinar on Persistent Identifier Selection by Marcel Ras and Remco van Veenendaal.
Below are some of the most commonly seen PIDs for publications and data:
Example - hdl:2381/12775
Non-commercial identifier resolution system, established in 1995 and operated by the Corporation for National Research Initiatives (CNRI). Used as the foundation of other higher level systems such as DOI. Commercial Handle licences can be obtained by research bodies and institutional repositories to establish local Handle systems, such as the European Persistent Identifier Consortium (EPIC).
DOI - Digital Object Identifier
Example - doi:10.1186/2041-1480-3-9
Combines a metadata model with the Handle system as the resolution infrastructure (i.e. DOIs are built upon Handles). First introduced in 1998 with funding from the International DOI foundation (IDF). Became an official ISO standard in 2012 (ISO 26324). DOI Registration agencies are responsible for assigning identifiers. The DOI system is maintained and advanced by the IDF, itself controlled by its registration agency members. Using the Handle system, there is a central free worldwide resolving mechanism for DOI names which means that DOIs are self-sufficient and their resolution does not depend on a single agency. A standard metadata kernel is defined for every DOI name. Assigning DOI names typically involves a fee, dependent on the business model of the Registration Agency, but the resolution of DOIs is free.
URN - Uniform Resource Name
Example - urn:isbn:0451450523
Introduced in 1994, formalised in 1997 and is now an IETF standard. No central governance, no central resolving infrastructure. Used by major national libraries in Europe. ISBNs for books are part of the URN system. No licence costs involved for assigning URNs, but a URN registration agency needs to establish an assigning and a resolving infrastructure. The biggest initiative to harmonise URN registration in Europe is currently undertaken by the PersID project.
ARK - Archival Resource Key
Example - ark:/13030/tf5p30086k
Introduced in 1995. Not a formal standard but all ARKs follow the same structure and workflows. No central resolver - organisations can sign up to become Name Assigning Authority Numbers (NAANs) and run their own resolution infrastructure for ARKs. The system is run by the California Digital Library with dozens of NAANs worldwide through a combined ARK/DOI infrastructure EZID.