Renverser vs. répandre
In French, both renverser and répandre can translate to the English verb to spill, but they focus on different parts of the accident. The word renverser focuses on the action of knocking over a container, while répandre focuses on the liquid itself spreading out over a surface.
Renverser
The word renverser is used when a spill happens because a container is knocked over, tipped, or flipped upside down. It focuses on the physical action of upsetting the object holding the liquid, which ultimately results in the spill.
Je viens de renverser mon café sur mon clavier.
(I just spilled my coffee on my keyboard.)
Le serveur a failli renverser le plateau de boissons.
(The waiter almost spilled the tray of drinks.)
Fais attention à ne pas renverser la peinture sur le tapis.
(Be careful not to spill the paint on the rug.)
Elle renverse toujours son verre d'eau quand elle est distraite.
(She always spills her glass of water when she is distracted.)
Nous avons renversé le seau d'eau en nettoyant la terrasse.
(We spilled the bucket of water while cleaning the patio.)
Répandre
The word répandre describes the liquid itself escaping its container and spreading across a surface. It focuses on the messy result of the spill and how the substance scatters, rather than the action of knocking something over.
La bouteille s'est cassée et le sirop s'est répandu par terre.
(The bottle broke and the syrup spilled on the floor.)
En trébuchant, il a répandu de la soupe partout sur la nappe.
(By tripping, he spilled soup everywhere on the tablecloth.)
L'encre de mon stylo s'est répandue dans tout mon sac à dos.
(The ink from my pen spilled all over my backpack.)
Le camion accidenté a répandu des milliers de litres de lait sur l'autoroute.
(The crashed truck spilled thousands of liters of milk on the highway.)
Le tuyau percé a répandu de l'eau sale dans toute la buanderie.
(The punctured pipe spilled dirty water all over the laundry room.)
Summary
To summarize, you should use renverser when you want to describe knocking over a container which causes a spill. On the other hand, use répandre when you want to emphasize the liquid itself escaping and making a spreading mess across a surface.