What I'm thinking is not simple to say, or type. I'll put it another way.
Time slows down near any physical object with weight, for smaller physical objects the difference is insignificant, but still there. If you are in the same place where time is being slowed down, everything's speed will decrease including yourself. Since you have been slowed down (thought processing, movement, the whole lot) you won't notice the time difference.
Say there is empty space, and then a black hole a few thousand miles away from that empty space. Time around the black hole will be noticeably different due to the gravity impact of the black hole. Imagine you threw a soccer ball towards the black hole from the empty space and waited for the ball to arrive at the black hole. (it will take a long time to arrive). Since there is nothing slowing the ball down, it will continue to travel to the black hole.
When the ball is caught in the black holes gravity, it will be pulled into the event horizon. Time around the black hole will be slowed down, and so will the ball. You are still watching from the empty space. The ball should speed up while it is sucked into the event horizon, but since time around the black hole is slowed down, the ball will be slowed down too from your POV. From the ball's POV, time is running normally.
With time being different everywhere, it is impossible to tell if our surroundings are slower or faster than times normal flow without atomic clocks or viewing a massive gravitational time distortion around a massively dense and heavy physical object.
Time on Earth is slower than the space above because of Earth's gravity. Everything on Earth is affected by this 'slowed time' effect, including us.