They are definitely different people and should not be merged.
Both are enumerated as separate heads of household on the 1860 Census (links below), one married to Harriet and the other married to Rachel.
However, the following issues remain and are probably the source of some confusion.
1. The so-called William Griffin Snider seems to go by the name Griffin, at least on multiple censuses. Suggestion: change his profile name to Griffin until someone can provide a source that his given name was, indeed, William. And, a findagrave page for an "unmarked" grave without a photo of a marker really isn't a source for this particular fact.
2. Griffin Snider appears in the household of the father, William Snider, in 1850, so it is a reasonable assumption that he is the child of William. Nonetheless, a confirming source should still be found.
3. William Snider may or may not be the son of the father, William Snider. A confirming source should also be found for this. Based on location alone, it is possible, and probably even highly possible, that William and Griffin are both the sons of William Snider but without proper sourcing such an assertion will always be conjecture.
William Snider - 1860
"United States Census, 1860", database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:MXFK-VCJ : 26 July 2017), Wm Snider, 1860.
Griffin Snider - 1860
"United States Census, 1860", database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:MXFK-FZK : 26 July 2017), Grifin Snider, 1860.