"Seize the night" vs. "Enjoy the night"
Solution 1:
"Seize the night" comes from the Latin carpe noctem which is a pun of carpe diem (seize the day).
It comes from:
Carpe diem, quam minimum credula postero
Which means:
"Seize the day while trusting little on what tomorrow might bring."
(From Horace, Odes I.xi.8)
It essentially means: Live today as if it's your last.
So, seize the night, in the context of the song, means: Live (party) like it's your last night.
Solution 2:
to seize, to take possession of, to grab.. to convey the idea of owning the night, a figurative way to say to live the night fully, to get the best out of it.
Solution 3:
Seize in this case is used for "embrace". It implies more emotional energy than "enjoy"
Solution 4:
"Seize the night" is obviously a take on "Seize the day", which comes from the Latin expression "carpe diem". That is a well-known saying with a specific sense, so outside of that expression, you cannot generalize "seize" to any other meaning than "to take."
Solution 5:
"we are only young if we seize the night". Seize: to use legal or official power to take (something). In this instance it would be, we are only young if we take control of the night. Which probably accounts for the title of the song "We Own the Night".