If you're talking about labeling things that belong to the user, and your site or app is supposed to feel like the site or app itself belongs to the user (their space), go with what the user would label them. For photos, what would the user write on a shoebox of their own prints? Most likely “My Photos”, but they also could just “Photos” if nobody else's things are stored anywhere nearby.
If the app or site does not belong to the user, but is clearly a third party the user gives things to in order to process them or perform some action on or with them, label it as a service person would speak to the user. How would the service person at Costco refer to those same prints? Probably “Your Photos” in contrast with "Everyone's Photos". In this case, the label "Photos" would be most likely to apply to all photos, not just the user's own.
Going with conversational style, keeping in mind who is the speaker for a given action, goes a long way to clarifying which stories need which terms.
This gets more complicated in "the cloud" but the same distinction (ownership vs operation, and who is the speaker for an action) can apply.
If the app or site does not belong to the user, but is clearly a third party the user gives things to in order to process them or perform some action on or with them, label it as a service person would speak to the user. How would the service person at Costco refer to those same prints? Probably “Your Photos” in contrast with "Everyone's Photos". In this case, the label "Photos" would be most likely to apply to all photos, not just the user's own.
Going with conversational style, keeping in mind who is the speaker for a given action, goes a long way to clarifying which stories need which terms.
This gets more complicated in "the cloud" but the same distinction (ownership vs operation, and who is the speaker for an action) can apply.