The Take Cover Basic Action states:
Source Core Rulebook pg. 471 4.0
"Requirements You are benefiting from cover, are near a feature that allows you to take cover, or are prone.
You press yourself against a wall or duck behind an obstacle to take better advantage of cover. If you would have standard cover, you instead gain greater cover, which provides a +4 circumstance bonus to AC; to Reflex saves against area effects; and to Stealth checks to Hide, Sneak, or otherwise avoid detection. Otherwise, you gain the benefits of standard cover (a +2 circumstance bonus instead). This lasts until you move from your current space, use an attack action, become unconscious, or end this effect as a free action."
Cover States
Source Core Rulebook pg. 477 4.0
"Cover is relative, so you might simultaneously have cover against one creature and not another. Cover applies only if your path to the target is partially blocked. If a creature is entirely behind a wall or the like, you don't have line of effect and typically can't target it at all."
Are "the benefits of standard cover" gained through the use of the Take Cover basic action relative like normal cover?
Yes, take cover has a requirement and that requirement must be fulfilled at all times to gain the benefit. They are not prerequisites, which is a separate game term for this reason.
I gave the example in a recent very similar thread of the raise a shield action, it requires you to be wielding a shield. If you then take off that shield, even though the raise a shield action says you retain the circumstance bonus until the start of your next turn, you will lose the benefit as it is a requirement for the action. Not a 1:1 example but does the job.
In addition take cover provides you an upgrade to your cover, so if it upgrades you to greater cover from one angle. It, may upgrade you to standard from another and none from another. It is inherently flexible because it has to be. It also remains in effect all round so if you are shoved prone, you will gain the effect, as well as if an ally uses an ability that creates something that satisfies the requirement. (You do need something to take cover with to start with though.)
Yes, to take cover you need to have an obstacle between you and the attacker that could be providing cover. And if the enemy does something - like Stride - that causes the obstacle to no longer be between you and them, then you lose the benefits of cover immediately against that enemy.
It is also possible to use Take Cover to gain or improve your cover against one enemy because the obstacle is in the correct position, but against another enemy you would not have cover.