On many websites you have a settings section where you can view and edit your profile data. On others you can edit your account data. Some sites even have both.
What is the difference between "account" and "profile"?
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Profile typically includes information about you that is displayed publicly.
Account typically includes information you need to share with the company for them to provide you services.
Ex. An ecomm site might store your name in your profile and your payment info in your account.
A person's profile provides a "a concise biographical sketch" (Merriam-Webster). In this context it probably contains name and address information.
An account usually contains details of transactions and the business relation with a customer.
If I were to make a purchase at an online store, I would expect it to be logged in the account. If I need to update my email address I probably need to make that change in the profile.
Now as you experienced the semantics are a bit vague and the distinction is not as useful for me as a customer as it is from the perspective of the system's database design. It's usually better to collect all information relating to the customer in one place and labelling it in a way that is more easily understood. And you could make the labels supportive of common tasks like changing addresses or checking purchase details. E.g. "your address", "recent purchases", etc.