The GDPR exhaustively covers the responsibilities and accountability of a Controller and Processor in several of its Articles, including Transparency, Risk Assessment, Data Protection Management and Individual Rights (Access, Portability, Correction, Objection, Erasure).
By definition, the GDPR defines a Controller and Processor as follows;
" ‘controller’ means the natural or legal person, public authority, agency or other body which, alone or jointly with others, determines the purposes and means of the processing of personal data; where the purposes and means of such processing are determined by Union or Member State law, the controller or the specific criteria for its nomination may be provided for by Union or Member State law; " [GDPR Article 4, Paragraph (7)].
" ‘processor’ means a natural or legal person, public authority, agency or other body which processes personal data on behalf of the controller; " [GDPR Article 4, Paragraph (8)].
Basically, on a web site, someone (the Controller) has to give permission and direction to other vendors (the Processors) to process the trove of personal data, which on a web site is seemingly endless.
The GDPR references the use of online identifiers, most of which would be transferred and collected by visiting a web site. "Natural persons may be associated with online identifiers provided by their devices, applications, tools and protocols, such as internet protocol addresses, cookie identifiers or other identifiers such as radio frequency identification tags. This may leave traces which, in particular when combined with unique identifiers and other information received by the servers, may be used to create profiles of the natural persons and identify them. " [GDPR Citation 30 ]
In addition to this, the GDPR specifically addresses the tracking of online activity, "... In order to determine whether a processing activity can be considered to monitor the behaviour of data subjects, it should be ascertained whether natural persons are tracked on the internet including potential subsequent use of personal data processing techniques which consist of profiling a natural person, particularly in order to take decisions concerning her or him or for analysing or predicting her or his personal preferences, behaviours and attitudes." [GDPR Citation 24 ].