I'm not sure what you're thinking, but the key difference between Newton's first law and Newton's second law is that Newton's first law tells you that inertia exists, and Newton's second law tells you how much momentum of an object changes when you exert a force on the object. They're not equivalent.

Well, the way Newton laws are thought in US schools is weird, and it creates a lot of confusion. The original newtons laws are ais they thought in schools, but nobody teaches the Scholium that precedes the laws.

In the Scholium Newton talks about absolute and relative motion. He mentions absolute coordinate frame, defined by immovable stars. Other frames are relative. Newton says that you cannot really distinguish two relative motions when forces are not actet on two objects. But if you connect these objects be a string and make them spin, by observing the tension of the string you can distinguish that spinning motion.

What Newton actually talks about in the Scholium is about inertial frames of reference, and all other laws can be applied only in such frames (actually Newton thinks that there is one true non-moving frame of reference).

These definitions in Scholium and explanation when we can replace absolute motion with relative motion is quite important. So in some other textbooks they are included as the first Newtons law, which is condensed to "all mechanical processes in inertial frames flow the same", or that "all inertial frames are indistinguishable". This definition of inertial frames may sound confusing at first, but it makes a lot of sense the more you think about motion and general applicability of Newton's laws. You can think about inertial frames as frames that stay in rest or move with constant velocity relative to each other.