Learn English – the difference between ‘secure’ and ‘secured’

Originally, cool meant someone who was somewhat standoffish in their demeanour, or someone who does not get too involved - and cold was just a more extreme form of that.

As Bill Franke points out, the meaning of cool meaning popular or trendy probably originated with cool jazz in 1945 and began being used to describe people in the 1950s seeing a rise in usage through the 1960s and a large spike in popular usage in the 1980s and 90s:

For this reason, "he's a cool guy" in modern English means "He is a trendy (or fashionable) person" rather than "His character is standoffish", whereas the meaning for cold never evolved to mean trendy, and retains its older meaning of someone who is very detached and unemotional.

If you want to use cool in the sense of someone who is slightly unemotional, you might prefer to use the idiom He's a cool cat or He's a cool character which both retain the old (non-trendy) meaning of the word cool. Alternatively you can say something like His response was somewhat cold as a less ambiguous alternative to His response was cool.

The two words you have chosen to define are particularly difficult to pin a definition to. If you were to ask this question on the Philosophy Stack Exchange you could get references to thousands upon thousands of pages of philosophy on the concepts. That philosophical basis helps shape the meanings of the words, so it is very hard to define them without at least touching on philosophy.

As such, you will find my wording choices waver, even in this answer. While it seems natural that the two words might have clearcut definitions, in reality the truth is that people mix their meanings all the time. (Forgive me, I know that sentence construction was cruel and unusual)

I believe the trick to understanding the words is that, when you use them to refer to a statement within language, the line between the words is murky. Accordingly, I'll explore their differences first, and then we'll bring them together.

Truth is typically considered an abstract concept. It doesn't "exist" anywhere, unless you have a religious belief which can point to a truth in reality. 1+1=2 is true, even though 1+1=2 is an abstract concept. We might argue that you can demonstrate its truth using real objects in reality, such as taking one stone and putting it next to another stone, and calling that "two stones." However, as we go deeper into mathematics, we find truths which are increasingly difficult to argue are part of "reality." For instance, a² + b² = c² when referring to the side lengths of a right triangle is a true statement, even if one never constructs a physical triangle in reality. In fact, we can make true statements about really unusual mathematical concepts that can never be physical such as Graham's number such as "the last 6 digits of Graham's number are 195387," even though Graham's number is so mindbogglingly big that it is actually impossible to write down directly in reality (the number is so much larger than the number of atoms in the universe that it actually hurts).

On the other side of the argument, it is possible for things to be "real" but not "true," and at this point I'll start trying to do comparative pairs of sentences to help try to explain the difference. A "real" thing is not considered "true" until it is assigned a truth value. People, for example, are typically not assigned a truth value. If I were to talk about an individual in history named Jesus, I would say "Jesus was real" or "Jesus was not real." I would not say X"Jesus is true" or X"Jesus is false," except in the most informal of ways (some will use the questionable construction "Jesus is true/false" as a shortcut for saying "The abstract content of Jesus's message is true/false," just showing once again how murky the line is).

The two words get very very very similar when discussing statements. Statements we have made span the gap between the abstractness of truth and the concreteness of reality. I don't believe I can do this topic justice in a SE answer. The way those words bob and weave within the context of statements is something you'll just have to learn on your own. Fortunately, in that narrow context English speakers will be willing to accept both constructions with little to no confusion.

One of the more interesting lines that gets drawn between the words is the idea that truth can be conditional, but there is only one reality. This is an assumption made in the vast majority of English speaking countries. I can make a statement about the truth-hood of a mathematical proposition within some defined bounds: "It is true that water brings life (truth statement), assuming it does not drown it first (context)." In that sentence, I was able to use the word "true" in a conditional sense. I cannot do that with reality, on the assumption that there is only one reality. This behavior can be seen in a compound statement, "It is true that water brings life, assuming it does not drown it first. However, in reality, the dam upstream is about to burst, and it will drown us if we stay here."

And, frustratingly, the story doesn't end there. The words continue to dance in a strange loop. Because the concept of "in reality" got so over used, we started to question the assumption that there is only one reality. We developed constructions using the phrase "my reality" or "your reality," and typically they are used with the assumption of one "truth!" Gads! Thus you will come across statements like, "Maybe in your reality you can act any way you like, but in truth, there's only one way to live."

And so, I believe I have given you lots of information, but its unclear whether it has actually helped. The best advice for understanding them I can give, in context of all I have written, is to use "true" when dealing with abstract concepts, and "reality" when dealing with concrete physical concepts. In the murky region inbetween, use context: determine if the current conversation suggests "one reality," which is the default for most English speakers, or if it suggests "one truth," and then use your words accordingly.