In short - not really, although they are of course very closely related.
If you ask me - Self-Harm can be described as "The act of doing something harmful to oneself for a purpose" - which is kept very generic for good reason. There are few subjects with quite so many reasons, triggers, causes, solutions - and so few clear answers that making a defintion more specific means you can be certain your leaving some minority group out.
Self-Harm is the blanket term for causing harm to yourself - and this does not nessesarily mean taking a blade to your skin. It might not have occured to many - but almost without exception, everyone around us, even those who mock or shun self-injurous behaviour self harm many times every day.
Smoking because you are stressed, drinking for dutch courage or taking drugs for escapism are all very much forms of the term Self-Harm, as described above. Each time a person decides to perform that action, they weigh the specific needs of that time "I really need a drink after today" above the risks of that activity that are directly known to them.
Self-Injury is really just another sub-catorgory of self-harm. It is a method of self harm as much as all the others - which is why self injury is Self-harm, but Self-Harm isnt nessesarily Self-Injury.
Harley