Archives often belong to public authorities that will store research data for a long time, often providing some governance and an obligation for e.g. migrating data to never file formats if needed.
Local, external storage refers to memory cards, USB sticks, drives etc. They are easy to remove and/or replace in a device, and can be used in e.g. a card reader, connected via USB etc.
Network drives are provided by your institution and accessed by a network drive path like e.g. \\files.myinstitution.edu\myusername
Not ready. External repositories are ….
Laboratory equipment refers to machines and similar that store data from e.g. measurements. This can either be stored on the equipment and transferred, or displayed to the user for manual reading.
Mails refer to your e-mail system, where research data can be contained in e-mails, or attached in files to an e-mail. This can be your institutional e-mail system, your own, or one offered by a commercial service provider like Gmail.
Video data can be stored in a folder on your computer on the build-in hard drive. This is often the case if you are working with very large video files, or are situated in a video laboratory.
Your university might have a repository for data and/or publications, where research data can be stored. In some cases, the repository can offer exposure of the research data through a data portal. Thus, an institutional repository is not always merely intended for public display of the data sets.
Cloud storage refers to solutions where the storage is available as a service. This can be commercial providers like DropBox, or institutional solutions – or somewhere in between. Common to the solutions will be an app, or utilizing a standard protocol, for providing access to files that are not stored on your device, e.g. your laptop or phone. However, often the cloud storage solution will synchronize the files – or at least need to copy them on a case by case basis – to be able to provide access.