They do sort of I know but there are some obvious things to look out for,
...PayPal will always use your full name. The scammers emails usually start "Dear Customer" or "Dear PayPal member" or similar as they don't know your name.
Spelling mistakes or grammatical errors as obviously PayPal check for that before sending their messages to their customers.
Some of the scam PayPal emails don't even bother to try & have an email address that even looks like it's from PayPal or even have the word PayPal in it (but some do so still be wary).
Some of the messages are sent to multiple recipients, ..again PayPal won't do that especially with regards to any account issues.
Also I just ignore any supposed PayPal message stating "there is a problem with your account" or "we've noticed suspicious activity on your account" blah blah blah etc with "click on this link" etc in the email message.
Instead (if I even believed it for a second) I will just go to my known secure PayPal saved bookmark on my toolbar and log in securely to PayPal through that. If there is any genuine issue with my account PayPal will tell me after I've logged in.