Why do reactants have higher enthalpy but lower bond enthalpy in exothermic reactions?

[GeneralOJB]

Am I right in saying that, in an exothermic reaction for example, the reactants have a higher enthalpy, and the products have a lower enthalpy, as seen from the energy profile diagram.
But the reactants have a lower bond enthalpy, and the products have a higher bond enthalpy, because a lower amount of energy is required to break the bonds in the reactants, but a higher amount of energy is released when the new bonds are formed. This just confused me as I thought enthalpy and bond enthalpy were the same thing!

 

[AGNuke]

During the course of reaction, the internal energy, and by extension, enthalpy, changes.

For e.g. During a reaction, the energy first increases to a certain maximum level (Difference in energy is called Activation Energy) then it comes down. (You know the bell-shaped graph)

The reactions doesn't takes place in arithmetic method. Even if burning is exothermic, it doesn't mean that we do not have to provide energy to do it.