Well, despite over 11,000 hits on Google for פח השמן (!!!) the correct spelling is פך השמן (which sadly only has 3000 more sites on Google.)
What is the cause of the confusion? It seems to me that besides both פח and פך being homonyms to most Israelis, in Modern Hebrew they both can refer to kinds of containers. Let's see how.
The word פך means "flask, jar, cruse". It appears three times in the Bible. Klein writes that the name is probably of imitative origin. Kil mentions this in the Daat Mikra on Melachim II 9:3 - when pouring from the jar it would make a pach-pach-pach sound. In Yechezkel 47:2 we find the phrase מַיִם מְפַכִּים - gushing water, which Kil says indicates the sound as well. (It should be noted that Kaddari and others write that the verb פכה derives from the noun פך ).
What about פח ? It originally meant "a thin plate of metal", and appears twice in the Bible (Shmot 39:3 and Bamidbar 17:3) - where the metal is gold or copper. Stahl writes that perhaps this word too is of imitative origin - from the pach! sound made from hammering the metal.
However, in modern Hebrew the word פח means "tin". I'm not sure how this developed. My first theory was that perhaps this was a misreading of Rashi on Bamidbar who uses the Old French word tenves to describe פחים . The word means "thin", but in Hebrew is spelled טינבי"ש - maybe someone saw the word "tin" in there.
But I've since noticed that the original (and more official?) word for tin is בדיל - b'dil. So perhaps pach went from "thin metal" to tin, in a similar process to the word "tin" in English:
In modern times, the word "tin" is often (improperly) used as a generic phrase for any silvery metal that comes in thin sheets.
From pach as "tin" we get pach as (metal) garbage can, and pachit פחית as (tin) can- even though most garbage cans are made of plastic, and the cans are made of aluminum. But both terms are types of containers, which probably leads to the confusion of spelling פך השמן.