Convert pg/mL to/from pmol/L? In this article, 148 pmol/L is said to be equivalent to 200 pg/mL.

But this unit conversion site says that 200 pg/mL are equivalent to ~734 pmol/L, and this one gives 44 pmol/L for the same value.

What am I missing here? What is the correct way to perform this conversion, and why are different sites giving back different values?
Your question is how to do the conversion of the units of mole/liter to gram/liter. 
Mole/liter, written as mol/L, is an amount (in units of mole) per liter.

To do this conversion, we need to know the convert mole to gram or vice versa.

To this end, we need to use the physical property of molar mass in units of gram/mole. This is the mass per mole of substance, in your case the substance is Vitamin B-12. 
According to Wikipedia, the molar mass of Vitamin B-12 is 1355.37 g/mol.

$$\frac{200\times 10^{-12} \frac{g}{mL}}{1355.37 \frac{g}{mol}}=0.146\times10^{-12}\frac{mol}{mL}=146\times10^{-12}\frac{mol}{L}=146\frac{pmol}{L}$$