Music plagiarism?

I blogged about this sad song...

...only to realise, thanks to my niece Chloe,  that the introduction sounds exactly like Say Something, which I also blogged about on my melancholic playlist. 

Can this be considered as music plagiarism? After all, is it just playing one note and then one chord in an even tempo. 

And I do wonder how wide can differences in melodies and tunes be, since we are limited to so few notes and chords, in that a composer may accidentally or unconsciously compose something that is already been composed by someone else. 

What do you think? Have you ever heard any songs or music that are similar?

pearlie