By the 5th edition D&D rules, the terms “short rest” and “long rest” have specific meanings. I won’t repeat the rules here except to say that PCs get certain benefits from these rests and those can vary depending on race, class and certain other features of the game.
Short rests require an hour of relatively light activity -- eating, talking, etc. Long rests require 8 hours (minimum) of rest -- typically sleep with only a couple of hours of light activity during that period.
I start by assuming a normal day. Unless the players tell me differently, I will assume that the characters camp for the night from 10pm to 6am during which time they sleep, eat, meditate, pray, tend to weapons and armor, clean up, tend to wounds, etc. I will also assume that you take turns being “on watch” during the night. If something happens during the night you can randomly decide who was awake and alert at that time. I also assume that the last hour (from 5am until 6am) you will be eating breakfast, preparing spells, packing gear, putting on your armor, cleaning up the campsite and preparing for the day. Later you will take an hour for lunch (noon), and dinner (6pm). Unless something happens to disrupt this schedule it gives the party a short rest at noon and 6pm each day and a long rest each night from 10pm until 6am.
I leave it up to players to track their hit points, spend hit dice during short rests to get back hit points, and note which abilities or spells you get back during your short and long rests. For example, if you are traveling along and run into some gnolls in the morning, I'll let you know it is 10am. If you continue along the road and arrive at a farm, I'll let you know it is say 3pm. You can then assume that the party rested for lunch at noon. I'll give anyone a few seconds to do paperwork if you need to... before describing that the farmhouse is on fire and more gnolls are killing the livestock, etc.
If a group specifically says they stop and take a short rest. Fine, you can take as many short rests as you want. I'll make note of the time and see if that affects anything (like the bad guys getting away, a second group of gnolls catching up to you, etc.). If a group says they don't rest (say they push on through lunch), then I'll make a note that you might arrive an hour sooner and it is up to you to know you can't recover any short rest hit points or abilities. If something is unusual, I'll remind you when scheduled short rests (lunch, or dinner) happen and confirm that you aren't stopping. For example, if you receive a letter telling you about an assassination across the city at 11am and it takes two hours to get across the city, I'll remind you that you are missing lunch.
The official rules say that you can’t benefit from more than one long rest in 24 hours. By that rule, if your last long rest started at 10pm your next long rest can’t start before 10pm tonight. I am a little more lenient than that. You can’t have more than one long rest per day. As long as that long rest doesn’t start more than 8 hours before midnight your fine. So it could start at 4:00pm, 5:00pm, 6:00pm … anywhere up ‘till 12:00 midnight. If you are not in a hurry you might even make camp an hour of two before your “long rest” and take an additional hour or two after to break camp, but that is entirely up to you.
The important thing to remember is that you can’t get the benefit from a “long rest” unless it is 8 hours long and you only get one of these each day.
Note regarding Elves: Even if you are an Elf and your 4 hours meditation gives you the same benefit as other’s 8 hours sleep, you still only get the benefit of a long rest if it is 8 hours long.