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You may need to check your settings on both services to make sure you have chosen the correct time-zone. If you're in a country that doesn't observe DST, make sure you select the correct time-zone or un-tick the box to adjust for DST. I honestly don't use Facebook or Twitter (I'm a bit of a paranoid security geek), but I do know that Facebook won't let you change your time-zone after your account is set (Facebook Help Centre). And Twitter, on the flip-side does "hours ago..." rather than a specific date/time. There might be an account-setting that adjusts that to your local time-zone, but that's up to you to look for.

They use Facebook's JS library to authenticate and use the available data to sign in to their website. The cookie is not shared. Sites like Yelp may use the data provided by the JS library to create new session/cookies and use that to detect if you've accessed that site later on. More details can be found in Facebook's documentation.