Before turning to the symbols, think first about the difference between something being true, plain and simple, and something being logically true (true as a matter of logic).
It is plain true that I'm less than six foot tall. But that's not a matter of logic: it's just a contingent fact about how things have turned out. (A few growth supplements when I was small and things might have turned out differently!) Compare the proposition that I'm not both less than six foot tall and taller than six foot. That uninformative tautology is true as a matter of logic. However things go with the contingent facts it will remain the case that I can't be both less than and taller than six foot tall.
Similarly, it is true that if I press this switch the light will go on. But that's contingent, it just happens that the wiring goes like that, there isn't a power cut and so forth. It's not a matter of logic that light-switches work. Compare: it is logically true that if I press the light switch and turn on the coffee machine then I press the light switch. There is no logically possible way that the antecedent of that conditional can be true and the consequent false.
Similarly again here. Define the so-called material conditional $A \to C$ to be equivalent to $\neg A \lor C$. [And let's not tangle now with the question of quite how the material conditional relates to the "if ... then ..." of ordinary language, as this isn't the key thing that is being asked for here.] Then with $A$ for camels have feathers and $C$ for Michigan has a lot of great lakes, it is plain true that $\neg A \lor C$ since both conjuncts are true and $\lor$ is inclusive, and hence -- trivially, by definition -- $A \to C$ is true too. But $A \to C$ is not logically true. We could imagine a world I guess where camels evolve to have a feathery coat, and the topography of Michigan is different so it has a lot of little lakes instead.
In logic we are concerned with what follows from what; so we are going to be interested in cases when, if a given $A$ is true, then $C$ has to be true as well as a matter of logic. Let's use $A \Rightarrow C$ to express this strong relation between $A$ and $C$. Then, at least as a first approximation, we have $A \Rightarrow C$ just when it is logically true that either we don't have $A$ or we $C$ together with $A$, which is equivalent to
$A \Rightarrow C$ just in case it is logically true that $A \to C$.
Now, with the camels/lakes readings for $A$ and $C$, as we saw, although it is plain true $A \to C$ is not logically true. So $A \Rightarrow C$ comes out false.
Of course, we'll want to fancy up our definition of $A \Rightarrow C$ so as not to rely on the intuitive notion of logical truth, so we'll perhaps want to define it in terms of their being no interpretation/model on which $A$ comes out true and $C$ false, where we give a fancy account of interpretations. Or we might give a definition along the lines of, for every substitution for the non-logical vocabulary in $A$ and $C$, $A \to C$ remains true. But that's fine tuning. We've already said enough to see how $A \Rightarrow C$ and $A \to C$ [in one use of the notations] can peel apart.
