Whats a unit? new to (Lantis) vials, therefore syringes; only know pen "units"

Pretty simple plain question: whats a unit?!  
May seem like a dumb question, but 
 
is the "unit" I talk about when I tell my doctor, and the "unit" I dial up
on the Humulin Luxura  pen (3.0mL Humulin N insulin cartridge), and the
"unit" on the following syringes I just bought the same?
 
I've been injecting insulin from the (3.0 mL) pen for 15 years. 
Lately I've been using 36 units of Humulin N (bedtime).  All under an
endocrinologists supervision.  I get lows so:
I now have a (10mL Lantis) Vial for the first time, and I've been told to
try about 32 units to start out with.
So I bought whole syringes for the first time ever, as opposed to the
needle tips that just screw on the pen.  These first ten small syringes
are 8mm, 31 gauge, 30 "units".
Its all the pharmacy had.  I'll just eyeball an extra 2 units, maybe I'll
just take 30 anyways.
 
Do I fill the syringe up?  i.e. 30 is 30 cuz its same as 30?  Thats right?