Are ‘I work out every day’ and ‘I exercise every day’ exactly the same meaning?

nope bc i think exercisin n workin out r diff

Sometimes you need clarification on that. I work out every day I go to work.  Exercise usually means going to a gym or lifting weights (working & paying for it)

. I would rather get paid for doing it.

But in general they are interchangeable terminology talking about being active.

They're used interchangeably in American English. Though work out suggest exercising individuals muscles. Because of the phrasing used. Exercise is less specific. For example:

" See you later, I'm going to the gym for a workout".

" I get exercise by riding by bike" more general. "I workout by riding my bike". This is not said.

No, you can exercise lots of things but "work out" implies repetitive activation of certain muscles: push-ups, pull-ups, sit-ups... staying mainly on the same place.

Running, biking, skating, swimming are not called "working out"

Work out would make me think you go to the gym to get more pump

Exercise makes me think you go out in the street and walk.

They can mean the same thing, though if I said i exercised I would include in the gym but if I said I work out I wouldn’t have to include in the gym. 

Not exactly but effectively the same.  Not all exercise is a workout, and perhaps even not all workouts would be considered "exercise", but the two terms are used interchangeably for identical activities often enough that the differences are less important than the similarity.  The import of each is identical even if the specific activities might not be the same.

''Work out'' suggests that you go to a Gym

''Exercise'' could just mean that you go for a run or a walk.

Yes, they mean the same thing.

They mean the same to me.