Or rather, there's not something called "common flu" (there's something called "common cold" colloquially, but even that is a umbrella term for tons of viruses).

Now, regarding influenza (flu), the virus, as Wikipedia puts it "Influenza (H1N1) virus is the subtype of influenza A virus that was the most common cause of human influenza (flu) in 2009, and is associated with the 1918 outbreak known as the Spanish Flu."

So, yes, the H1N1 (1918) and the influenza A (most common modern variety of flu) are closely related types of the virus.