Is synechdoche the same as synecdoche without the"h"? Do they mean the same thing or what is the difference? Are the words used in different countries?
Wiktionary calls "synechdoche" an obsolete spelling of "synecdoche."
I would never use the spelling "synechdoche" and neither would any other English speaker, as far as I can tell.
I'd unlearn the spelling "synechdoche" altogether. What do you have to watch for is not confusing "synecdoche" with Schenectady, New York!