As I was reading about Newton's First Law of Motion from some textbook, I noticed some detail that seemed to conflict with another textbook which I have read previously. Book 1 provided the following statement for the law:
In the absence of external forces and when viewed from an inertial reference frame, an object at rest remains at rest and an object in motion continues in motion with a constant velocity (that is, with a constant speed in a straight line).
Furthermore, to prevent misconceptions, Book 1 even made sure to emphasize this detail regarding when the law applies :
Newton’s first law does not say what happens for an object with zero net force, that is, multiple forces that cancel; it says what happens in the absence of external forces. This subtle but important difference allows us to define force as that which causes a change in the motion. The description of an object under the effect of forces that balance is covered by Newton’s second law.
However, Book 2 on the other hand has this to say:
Law of Inertia. States that a particle remains at rest or continues to move with uniform velocity (in a straight line with a constant speed) if there is no unbalanced force acting on it.
Newton’s first law is a consequence of the second law since there is no acceleration when the force is zero, and so the particle is either at rest or is moving with constant velocity.
Now it seems to me that these two sources conflict with each other, in particular, the condition of whether the law applies strictly in the absence of any external forces, including forces that balance out, or whether it still applies as long as there is no net force. Also, Book 2 implies that Newton's First Law is a special case of the Second Law where acceleration is zero whereas Book 1 seem to treat the two as separate things.
My question is which one should I follow? Is one correct and the other wrong? Or does the difference even matter at all?
Edit: For those who are curious about the books I'm referring to, here they are:
(1) Serway, R. A., & Jewett, J. W. (2013). Physics for Scientists and Engineers with Modern Physics (9th ed.). Cengage Learning.
(2) Hibbeler, R. C. (2016). Engineering mechanics: statics. Pearson Education India.