Is there an Equality Between the Laws of Physics and Time?

Disclaimer: I am a total laymen when it comes to physics. Everything I say should be first assumed to be more pseudoscience than real science unless I can put forth the effort to prove otherwise. This is mostly just some musings and honest questions.

I was listening to this What is Time? lecture from Sean Carroll. In it he explained how the laws of physics do no dictate changes over space, but rather changes over time. That is to say that just because a certain scenario exists in one location of space,  that does not dictate what scenario should exist in some nearby location of space. Sure, given time, nearby locations in space effect the surrounding space. However, given a single moment of time the laws of physics do not dictate what scenarios can or cannot exist with respect to an interval of space.

Time however, is very different. The laws of physics do indeed dictate what can or cannot exist over an interval of time. Given the details of a certain moment in time, the laws of physics tell you what must have come before in order to produce that scenario, and what must come next. It would seem that this is the laws of physics by definition.

This got me thinking about the definition of equality. The laws of logic tell is that if you have two truth statements such that A is true if and only if B is true, then there is a logical equivalency between the two statements.

Let's apply this to the concepts of time and space. To start, lets think about a simplified scenario. If time stops and nothing changes, then there are no laws of physics that govern the passage of time. If there are no laws of physics that govern the passage of time, then nothing changes which implys that time has stopped.

Let us restated this more generically and hopefully with a bit more precision. Time is the change governed by the laws of physics of space and the things within space. The laws of physics is the change of space and the things within space over time. Again, this seems to be a logical equivalency between the laws of physics and time itself. Is this grounds to claim that time is not something within the laws of physics, but is the laws of physics themselves?

This brings to mind a few questions that we could ask:

1. If time is nothing but the laws of physics themselves, does this limit what the laws of physics can teach us about the nature of time? This is to say, if the laws of physics and time itself are inherently equivalent, does this push the nature of time itself out of the domain of physics?
2. How could this be affected by relativity? If we have a theory about the different ways time can pass for different observers depending on speed and gravity, does that not mean that we have a law of physics in regards to time? I have not had the ability to think through how these ideas would need modified to accommodate this.

Again, do not give me any benefit of the doubt in my scientific acumen. For all I know there are fundamental confusions about my understanding of physics. That being said, it is also possible that the questions I have raised could be provided with meaningful answers that may help laymen like myself develop a deeper understanding of physics.

Edit: It would seem that Sean Carrol makes a similar point when discussing Event and the Nature of Time. In that when the Schrodinger equation is taken at face value and treated as a true and fundamental description of the universe, time is invariably built into the equation that governs the universe. This is in contrast to the way the general relatively treats time as an emergent reality just like the spacial dimensions.