Logic is the basis of most things. The whole world is created of things that have been deemed "logical". It is probably most seen in math and it isn't a new notion. The Ancient Greeks used logic too! Even now, logic is used in programming. It is simply one of the building blocks of the physical world, but it itself is simply an idea. People generally apply logic in the real world to prove things that aren't basic facts. You can't grasp logic or see it, but somehow you just know when something is logical. How does that make sense? I don't know exactly, but I do have a definition of logic for you: Logic is the application of known facts and reasoning to come to a conclusion. It is usually the most plausible option or thing in a scenario and there isn't an exact reason, but sometimes it just clicks. You just look at the options and automatically choose one of them, thinking, "Oh, that's the most logical option." For example, if someone asked you whether the Earth was flat or round, you would say that it is round. If they asked why, you would say because the Earth isn't flat. If the Earth isn't flat, then therefore the most logical option is that it is round. And if they asked WHY it was logical, you would back it up with things like there are no edges of the Earth in which you can walk off of, which is a basic fact, and you can't just see the opposite side of the Earth. You could even say that even with the best telescope there is, yuo can't see the opposite side of Earth because the opposite of the Earth from wherever you are is on the other side of the planet. You use logic all the time in your daily life, and even now I'm using logic to explain to you what logic is!
Reasoning is very similar to logic, in that it is one of those things that are used to describe the world or figure out things. Many scientists and astronomers in Ancient Greece would use reasoning to create hypotheses. Like logic, reasoning is something that applies knowledge to the real world. It is also an idea, due to the fact that it is not tangible. Someone came up with the idea that you can take basic facts to prove another fact(logic) and that process of elaboration is what we call reasoning. It is simply a name for how you can reach the most logical explanation for something. This might just be going over your head and seem like a big cluster of confusing words, so here is a definition: The definition of reasoning is taking basic facts and one's known experiences and making observations based on those things. For example, if your friend asked you what the lunch was going to be today, you might say pizza. But, how did you know that? You used reasoning to figure out the most logical answer to your friends question. It may have smelled like pepperoni by the cafeteria, which made you think of pizza. This is a basic fact, that you can rely on. However, this is not a strong enough argument on its own. You may have also seen a pile of discarded pizza boxes outside of the cafeteria. This is also a basic fact because there is no denying that there is a pile of discarded pizza boxes outside of the cafeteria. This is enough evidence to safely reason that the lunch for today will be pizza. This may have happened very quickly in your head had it been a real-life situation. Humans are very intelligent creatures who can pick up many details and so, even though you don't think about it much, you are reasoning all the time! However, the Greek philosophers were answering more complicated questions, so they most likely did not go around sprouting theories left and right, but had to think hard about, gather evidence with a purpose, and even then, it might have taken them years to come up with a sound theory.