You'll usually want it the other way around: to sync <= to cache.
"To sync" -- how many most recent messages the app looks at, every time it checks mail, to keep up to date.
This is how many show when you open a folder.
About those messages, Aqua knows that 1) they still exist on the server and 2) their flags (read/unead, starred).
"To cache" -- older messages, previously synced as "messages to sync", beyond the *current* "messages to sync" setting.
Will now show when you open a folder -- since Aqua doesn't know if they still exist on the server, and their flags.
Will be used if you scroll down a folder to see more messages, to speed up the loading time.
Are trimmed from the device's storage automatically over time as necessary.