Patis: Our source for this word is the Malay / Indonesian term petis udang, shrimp paste. Shrimp paste is also called bagoong in the Philippines.
Bagoong / fish paste is made by storing fresh fish and/or shrimp with salt until it ferments. When the fish and/or shrimp is completely processed, a clear liquid rises above the fermented solids; this is the fish sauce, the patis.
Toyo: This is soy sauce, in general; it originated in China in the 2nd century and spread to many parts of Asia.
Chinese soy sauces are called jiàng yóu in Mandarin, jeong yau in Cantonese. In Japan, however, it has been called shoyu since the 7th century, when it was introduced to the country by Buddhist monks.* It is possible that our word toyo came from the Japanese, with whom we traded since before the arrival of the Spaniards.
Rafael Alunan writes in “The Philippines Before Magellan:”
Early Spanish documents reveal that, apart from Chinese junks, large trade ships from Borneo, Thailand and Japan dropped anchor in the coastal ports of Manila, Mindoro, Pangasinan, Cebu, Jolo and Cotabato. Filipino traders had significant knowledge of and presence at other Southeast Asian trade ports such as Melaka, Borneo, Ternate (Moluccas) and Myanmar.**
* Source: Wikipedia