Use [dicomweb] whenever talking about their specific sub-services: STOW, WADO, QIDO, UPS and in general about its RESTful interface. Countersense, DICOM can be used for discussing about the DCM storage format, and the communication services like C-STORE, C-FIND, C-MOVE, etc.
DICOMweb is the DICOM standard for web-based medical imaging. It is a set of RESTful services, enabling web developers to manipulate healthcare images using industry-standard toolsets. It is divided into STOW, WADO, QIDO and UPS sub-services.