Repairs simply repair damage to a given part. Overhauls not only repair the damage but bring the durability and primary stat (HP/Draft/Handling) to the level as if your crew chief built a part from scratch. This is why repairs are typically faster and cost less compared to an overhaul.
It should be noted that continually repairing a part will degrade it over time. The degradation can be seen in slight drops in the parts durability. (Note: If you purchase a car component and then overhaul it, the part's new characteristics will be based on your crew chief's current ratings. If your crew chief couldn’t have built a part as good as the one you purchased, the stats WILL DROP to that of which he could build.)