What is the difference between enthalpy of reaction and standard enthalpy?
Yes, the standard enthalpy of reaction ($\Delta_\mathrm{r}H^\circ$) is the enthalpy change that occurs in a system when matter is transformed by a given chemical reaction, when all reactants and products are in their standard states. The only condition is that the participants have to be in their standard states, ie. usually at 1 bar pressure.   

On the other hand, enthalpy of reaction ($\Delta_\mathrm{r}H$) is amount of energy absorbed or released at any condition. Considering your example, 
$$ \ce{N2 + O2 -&gt; 2NO} \qquad \tag{$H = \pu{+181kJ}$}$$ 
Here, $\Delta$H represents the amount of heat absorbed in the formation of 2 moles of $\ce{NO}$. For the formation of one mole of a substance from constituent elements, it is called enthalpy of formation($\Delta_\mathrm{f}H$)and if in standard states, standard enthalpy of formation.
$$ \ce{ 1/2 N2 + 1/2 O2 -&gt; NO} \tag{$\Delta_\mathrm{f}H$}$$
As we can see, $\Delta_\mathrm{f}H$ = $\frac{1}{2}\Delta H$. Hence it should be $\Delta_\mathrm{f}H$= +90.5 kJ/mol. 

Note: Unit of enthalpy is that of energy but unit of enthalpy for a reaction is of energy per unit mass or amount.