You can’t put a cap on a nap.
There simply is not a specific point that would explicitly define for every single person on the planet the length of a nap versus the length of a “sleep.” It’s silly to try and make arbitrary distinctions, saying that anything more than some random limit is regular sleeping but anything less than it is considered napping. Setting such a limit is just splitting hairs. For example, if you say a nap cannot be longer than four hours, can you really argue that there really is that much of a difference between sleeping for that set limit of four hours or instead sleeping for five?
Therefore, a nap is any time in which one is sleeping outside of their normal sleeping hours. If you typically are diurnal and then also decide to sleep during the day, whether you sleep for 20 minutes or six hours, that sleep is a nap. Similarly, if you are routinely nocturnal for any reason, for you, sleeping during the night is napping. After all, a person that regularly only sleeps a few hours at a time is not just repeatedly taking naps and never fully sleeping. What constitutes napping is personally defined by an individual, rather than constricted by societal norms.
Some claim that sleep is one’s “regular” resting time, whereas napping is whatever sleep falls without that time period.
It is clear that sleeping and napping are conventions, defined by speakers who use each of the terms, rather than by reference to any real concept in the world. These words are tools that people use to distinguish different activities. This is why I argue that, while napping and sleeping both refer to the same exact practice, namely, closing one’s eyes and entering a partially depressed consciousness in order to rest for a given period of time, the difference is that napping refers to the shorter, and sleeping to the longer period of time among the two.
When we say we’ve taken a “nap”, we aren’t referencing any norm of schedule in our sleep, to the extent that schedule describes specific hours. For example, suppose I usually slept from midnight to 8 a.m., and one night I had a plane flight from 2 a.m. to 5 a.m. If I rested on the flight, I could easily characterize that rest as a “nap” and all would understand my meaning. Notice, however, that the rest occurred during the hours I would normally be asleep. I’m able to refer to this as a nap because “nap” denotes a length of time. It doesn’t denote a specific length of time, but a lesser time than one is accustomed to sleeping, usually.
There is no rule denoting that a nap must be shorter than the amount of time you are typically accustomed to sleeping; and there really is no set indication that the term “nap” denotes any length of time. This is clear when people discuss how long a nap typically is for them, and the answers vary greatly. Similarly, imagine the situation in which I stay up very late one night to finish a project, and eventually end up getting only about an hour of sleep in total. The next day I would not say that I “napped for an hour last night,” but instead that I “only got one hour of sleep last night.” Thus, I add to my argument that one’s intentions as they go to sleep are just as important as the time of day. The difference between napping and sleeping is just like the difference between gossiping and venting. Whether you are gossiping or venting you are still talking about someone and likely doing so when they are not around. However, it is gossiping when you are intentionally derogatory and venting when you simply explain what happened. Likewise, while you end up asleep at some point either way, it is napping anytime you intend to rest outside of your usual nightly rest.
It is certainly better to say that “nap” simply connotes, rather than denotes, the meaning of a shorter period of time than “sleep.” But while the time one’s typical nap occupies may vary greatly, we would be shocked to meet someone whose nap extended beyond the length of sleep they typically take: hence why napping is the shorter activity.
Your example about sleeping only one hour is valuable to our discussion, but it doesn’t support your definition. What it evidently represents, along with my example of the flight-nap, is one of many situations in which we can’t find an exclusive definition of the two terms because their meaning is so similar and their descriptive powers overlap. In both cases, either term would communicate the meaning of the rest to a listener without problem.
With the addition of intent, your definition of napping has grown to an unstable mass and its application has shrunk far beneath the actual use of the word. First, according to you, the napper must intend to distinguish their rest from sleep, rather than using the two terms in an interchangeable context such as the plane-rest or the one-hour rest. Then, they must intend to sleep at a time which falls without their “usual” sleep schedule. But many do not have any usual nightly rest because such a period of time varies, sometimes greatly, each night and throughout weeks, months and years. What is described by a “nap” on one day would only be considered a “sleep” on a different day of the week, or vice-versa. Hence, you haven’t provided a necessary definition, only one that gestures towards the meaning of napping.
Regardless of the time of day, the intent of the napper, and their “usual” resting habits, the napper will always rest during periods of time less than the times during which they sleep. No other quality can consistently define napping.