Obviously. It's pretty straightforward.
A. Science is not scientists ---I don't understand.
Science is not scientists. It is a set of falsifiable theories. It is nothing else. No more. No less.
B. falsifiable theories. ---I don't understand--- should it not be "provable theories" [formal terminology is Okay. But non-intuitive terms should make sense]
No. Here's why:
An argument is a set of predicates and a conclusion. A theory is an explanatory argument. There are many theories, some of which are science. Only falsifiable theories are theories of science. So...what is 'falsifiable'?
It is a test to see whether the theory is bogus or not. The test is designed to try to destroy the theory. The test must be available, practical to conduct, specific, and produce a specific result. If the theory survives such a test, it is automatically a theory of science. It is automatically part of the body of science. It will continue to be so until a test is devised against the theory that succeeds, thus falsifying the theory and destroying it utterly.
All theories begin as circular arguments. This is not a fallacy. It is simply an argument that uses itself as a predicate. The difference with a theory of science is the test of falsifiability. It now has something more than just the simple circular argument to go on. No theory can be proven True, whether a theory of science or not.
A theory that is not falsifiable remains a circular argument. It can neither be proven True nor False. The other word for the circular argument is 'faith'. It is also called the Argument of Faith.
A religion can best be described as some initial circular argument, with arguments extending from that. Christianity, for example, has as it's initial circular argument that Jesus Christ exists, and He is who He says He is, namely the Son of God. ALL other arguments stem from this initial argument. The Church of No God is the same way. It's initial circular argument is that no god or gods exist. ALL other arguments stem from that initial argument.
Science does not use supporting evidence. Evidence is not a proof. Literally mountains of supporting evidence mean nothing in the face of a single piece of conflicting evidence. Science only uses conflicting evidence.
Only religion uses supporting evidence.
To attempt to prove a circular argument creates the Circular Argument Fallacy. This is what a fundamentalist does. There are fundamentalists in any religion. Some religions are inherently fundamentalist in nature, including the Church of Global Warming, the Church of Green, the Church of the Big Bang, the Church of Evolution, the Church of Creation, and the Church of No God.
Some people make the mistake that observation is a proof. Unfortunately, observations are subject to the problems of phenomenology. Data is the result of an observation. The observation itself, and the data it produces, is evidence only. It is not a proof.
Proofs only exist in closed functional systems like mathematics or logic. Science is an open functional system. It's only rule is that a theory must be falsifiable.
Since a theory is an explanatory argument, no theory may exist that stems from a fallacy (an error in logic), since such a statement is not a valid argument. All theories must conform to this. This is known as the internal consistency check. All theories, even nonscientific ones, must pass this check.
No theory of science can conflict with any other theory of science. One or both theories must be falsified. This is known as the external consistency check. All theories of science must pass this check. Nonscientific theories are not required to, since there is no test for them. They can neither be proven True nor False. Nonscientific theories simply exist...forever.
There is no method or procedure for science. The only requirement is that a theory must be falsifiable. A theory that has been falsified is no longer a theory. It is nothing. It is a fallacy.
A theory is nothing more than an explanatory argument. It cannot predict. It only explains. To gain the power of prediction, theories of science must turn to a closed functional system, such as mathematics, where the power of the formal proof exists, and with it, the power of prediction. Predictions in math? Example: if a=b*c and a is 10 and c is 20, what is b? This is what I mean. The value of 'b' can be predicted for any values of 'a' and 'c'.
When a theory is transcribed into mathematical form, this is known as 'formalizing' a theory. The result is an equation, also called a 'law' in science. If the theory is falsified, the 'law' goes with it. It is this 'law' that gives the theory the power of prediction.
Some well known laws of science:
The Theory of Motion by Isaac Newton: F=mA, where 'F' is force, 'm' is mass, and 'A' is acceleration.
The Theory of Stefan-Boltzmann: r=C*e*t^4, where 'r' is radiance (light) in watts per square area, 'C' is a natural constant, 'e' is emissivity, and 't' is temperature in Kelvins. This theory describes how light can be generated from a material at some temperature above absolute zero. It is, of course, not the only way to generate light.
The first law of thermodynamics: E(t+1)=E(t)-U, where 'E' is energy, 't' is time, and 'U' is work (force applied over a distance in a given time). In other words, you cannot create energy out of nothing.
The 2nd law of thermodynamics: e(t+1) >= e(t), where 'e' is entropy (the randomness or dispersion of energy or anything else), and 't' is time. In other words, you cannot reduce entropy in any system.
Ohm's Law: E=I*R and P=I*E, where 'E' is electromotive force (or a pressure, or voltage), 'I' is current (or amperage), 'R' is resistance or impedance (in ohms), and 'P' is power in watts (joules per second), or energy per second. In other words, voltage (pressure), current (or flow), resistance (or friction), and power (or work available) are all related. This equation works just as well on plumbing as in electronics.
All of these equations are formalizations of their underlying theories. Each of these theories is falsifiable. It is conceivable to conduct a test to try to prove the theory wrong. Such a test is specific and produces a specific result. If it disagrees with the equation, the theory is falsified. That test must test the theory itself. It cannot test a different theory. No test can prove a theory True.
Thus, theories of science are just that...theories. They are not a proof. Any one of them could possibly be falsified tomorrow. Until they are, they cannot just be discarded. They have something to go on beyond the simple circular argument.
Science and religion are both defined by philosophy. Philosophy is nothing more than a set of reasoned arguments. The only rule in philosophy is that you must present your own arguments. You cannot borrow from the arguments of others as your own. In other words, no cut and paste. Unfortunately, philosophy is not typically taught in schools (even colleges and universities), and so people have no idea what it actually is. A typical college or university 'philosophy' course introduces a smattering of paradoxes, has you write a few essays on them, and calls that 'philosophy'. It's garbage.
Philosophy teaches you how to think and reason for yourself. Along with logic and mathematics, it can cut through the fog like a knife. It's why the Greeks put such a high value on them. Today, these disciplines are rarely taught, if taught at all. Today is a world of illiteracy...not just in the United States, but in the UK, France, and even Germany as well. Even Greece has forgotten what they had, and now live in a world of illiteracy.
The United States is particularly bad. Cutting and pasting from websites and using these as an argument is extremely common. No reasoning is even given. The cut and pasted website is considered a proof in and of itself.
Hope this helps to clarify some things you don't understand about science and falsifiability, and why science is defined the way it is.