There are plenty of resources (printed books and online material) that describe the origin, evolution and study of surnames so I need not repeat much of it here. Suffice it to say that there are a number of basic principles:
Not everyone with the same surname will have the same origin because identical surnames can arise independently at different times and in different places.
However some surnames will have a single point of origin (in place and time). Even where this is true it does not always mean the people with that surname are blood related.
Surnames can change over time - in terms of their pronounciation and/or spelling, either universally or in subsets of those bearing the name.
It is only in the last thousand years or so that surnames have been patrilineal, i.e. passed from a father to his family. This is not always the case.
Surnames can be changed.
Surnames can be acquired by those other than blood relatives (e.g. adoption, use of mother's maiden name).
There aren't universal conventions about how a surname is spelled and what conventions there are can be violated by migrating to a new area with different rules, literacy, languages etc.
It is probably safe to say that all surnames start out with some meaning - that is they describe the bearer of the name - in terms of where they live, what they do or some characteristics of the person. The form that takes will be dependent on the local language spoken at the time. Sometimes the language dies out but the sound stays the same. It may be later adjusted to match words in the replacement language - e.g. Gaelic names become anglicised or the original meaning could be re-expressed in the new language. It is still the same surname in terms of indicating a lineage even though it may have changed beyond recognition from its original form.
References:
Family Names (Wikipedia)
Names and History: People, Places and Things by George Redmonds (ISBN 185285426X)