To carry something is to take or support it from one place to another. This very common verb does not, on its own, suggest difficulty or a high degree of effort; it merely states a mode of conveyance: I carried the casserole to the neighbor’s house. The synonym lug, on the other hand, suggests strenuous effort. This verb is used to talk about pulling or carrying heavy or ponderous things with force or great exertion. If you lug a suitcase up a flight of stairs, the suggestion is that you are transporting it, maybe even dragging it, with some difficulty. It’s no surprise that this verb is sometimes chosen to emphasize or even exaggerate the burdensome nature of a task.
In the most general sense, a mistake is an error caused by poor reasoning, carelessness, or insufficient knowledge. This finger-wagging noun can be applied to actions, calculations, opinions, or judgments: it was a mistake to argue. A snafu is an error, glitch, oversight, or misunderstanding that causes a confusing situation. A scheduling snafu at a restaurant might result in a table being overbooked—putting hopeful diners in an awkward situation once they arrive. Some readers might’ve experienced a technical snafu or two working from home and videoconferencing with their colleagues (is that mute button really on?). Snafu can also refer to the situation itself, more precisely, a badly confused or ridiculously muddled one: the ballot snafu led to a recount.
In the most general sense, a gap is a break or an opening. It can be a physical opening, like a gap in a fence, or it can be an empty space or interval, like a gap in a siren’s wailing. A gap can also be an interruption in continuity: a gap in one’s memory. Just like gap, the synonym chasm refers to an opening or break, but on a much larger (and considerably more ominous) scale: in the literal sense, a chasm is a yawning fissure or deep cleft in the earth's surface—you might also call it a gorge. But chasm is more commonly used to talk about situations in which there is a very wide distance, or more specifically, a marked difference between two things—almost to the point of being impossible to bridge or to bring together. You might encounter it used to describe an irreconcilable breach in relations marked by a divergence of opinions or beliefs between persons or groups (a chasm between the haves and have-nots).