Chances are, at least for most backpackers, the answer to this question is "it depends". It mostly likely depends on your goals for a particular trip or it may depend on who you're hiking with. But whatever the case, it's important to identify what style of hiker your are in order to properly prepare for a given trip.
So what is a "Trekker" and what is a "Destination Hiker"?
Trekker's are backpackers that hike for distance and speed. This is typical of thru-hikers. Trekkers absorb and experience the trail as it washes past them throughout the day. Trekkers will almost always hike more than 15+ miles a day on trail, and some thru hikers will hike in excess of 30 miles a day! To do so weight has to be managed carefully. Some, particularly Destination Hikers, scoff at trekkers suggesting they're missing out on the beauty of the trail but trekkers will tell you that's simply not the case. In fact, Trekkers often hike from early in the morning until late in the day allowing them to to see and cover much more ground thereby seeing more in a given trip.
Destination Hiker's are backpackers that are in the mountains for perhaps different reasons. Maybe it's about a fishing experience, photography, enjoying nature, maybe it's about enjoying family in a quiet, serene environment, or maybe it's that these folks just enjoy the camping part of the experience as much as the hiking. Destination Hikers plan their trips for shorter distances - generally under 10 miles and often in the 5-8 miles/day range. The goal isn't so much the hike but to "get to camp". Thus the term "Destination Hiker". Unlike Trekkers, Destination Hikers may wake up late(er), hike shorter days (generally under 10 miles) and seek to get to camp before 4:00, sometimes even as early as 1:00 or 2:00. Destination Hikers are more likely to take zero days (days where you don't hike at all) to enjoy a camp site whereas Trekkers will only take a zero day when absolutely necessary to rest.
The truth is many hikers may be both but at different times. The important thing to remember however is your trips should center on one of two of these two styles. The reason this is important is because how you pack/what you pack for a trip will change rather dramatically to suit one of these two styles.
So, why does it matter whether you're a Trekker or a Destination Hiker?
If you're a Trekker you want to travel far and fast which means you want your pack to be as light as possible - maybe even "ultra-light". Therefore trekkers have no need for ancillary equipment like fishing gear, large cook sets, binoculars, heavy camping equipment, etc. as you'll be getting to camp late and up early. More importantly the more weight you carry the more difficult it'll be to put in the miles. Trekkers will opt for tents and backpacks that are under 3 pounds or even under 2 pounds, gravitate towards quilts rather than sleeping bags, and some may even cold soak rather than cook meals (although the benefits of cold soaking may be overdone). Most Trekkers will focus on getting "base weight" (the weight of your pack less consumables) under 10 pounds.
If you're a Destination Hiker you're on a trip for comfort so a camp chair, fishing equipment, large cook set to make that special backcountry breakfast, maybe a large knife or cutting tool for fires, etc. may all be part of "necessary equipment". For Destination Hikers the focus is on the camping and recreational goals once you get to camp. The hiking is just a thing you have to do to get to camp. Heavier backpacks with proper frames and hip belts to distribute weight are necessary in order to manage the weight of all the equipment. Larger and heavier multi-person tents may required. Here base weights may be 20 pounds or even more.
The key take away here is to understand what your goals are for any given trip. You may be a Trekker when you decide you're going to take on the JMT or section hike the PCT. On the other hand you may be a Destination Hiker when you're out for a 3 day trip with the family and/or friends. Pack accordingly to ensure you have the best outcome and most enjoyment for your given trip.