Going off what others said, it's good and perfectly fine that you're high on objective damage and doing that versus having high damage output and fighting. Obviously when you said the support had more damage than you, I could ask if said champion was like Zyra or Brand, but that's not the point. As a jungler you want to get leads and advantages for your team, as well as aiming to get objectives. Playing the map is key to do so, which also means sometimes you won't be ganking or fighting, instead you'll be invading or setting up to take a tower, even split pushing in some cases. Are you just worried you aren't being impactful enough because of the damage you're dealing? If so, as stated before, it's perfectly fine because you're taking objectives and by doing so, getting your team closer to victory.
I don't know what you know or what rank you are at, but what I've learned is that there are a few essential things every good jungler (and player for some of these) should have and needs to know:
Vision control, importance of scuttle, pathing/jungle clear, understanding your champion, how to snowball a lead, awareness (map, CDs for sums, etc) build order, matchup and how to play against your enemy/counterpick. (that's all I could think of ATM)
To elaborate on a couple of these, I'd say having awareness and vision control is a priority, (besides literally knowing how to play your champion, but that's a given) It doesn't matter if you don't have the most efficient jungle pathing or whatever, with good awareness and vision control, you can take advantage of the enemy having no vision if you've pinked a bush to then "easily" gank someone, or take an easy drake if you've got lane priority and it's unwarded. Or even if the enemy jungler has just ganked top and you're botside, that's a drake the enemy jungler can't really contest, and if the mid and bot try and stop you, they've got two top so it's a 4v3 effectively (that's assuming both come, if lanes are shoved or they just recently backed, they can't make it in time or afford to go, especially if they're behind.) Plus, contrary to that, if you spot the jungler bot or top, you can invade and get in deep wards while they do so (if you can't stop them in time) or simply because that puts them behind and if your champion is strong early and theirs isn't, they know they can't invade your side to catchup. This is also why scuttle is important, as besides being super easy to kill, provides much needed vision and a mvmt speed buff in the river.
I really didn't pay much attention to CDs when I first played. Big mistake. I didn't keep track of who had flash up, who just used their utility/escape/cc, etc, and that really hindered how I was able to interact with the lanes and in getting leads. If you know the top laner doesn't have flash, and say they are Nasus or Darius, who don't have much in terms of getting out of a bad situation like Akali or Fizz or Tris, you can abuse that and do repeat ganks, or apply lots of pressure to take plates or topside obj., and/or force the enemy jungler to either focus more on mid or bot or come topside and help (same with mid roams) Even so, they can counteract that by warding more or playing more defensively, but that allows your top to take advantage of that in multiple ways. It's especially important in the early game, as before I wouldn't think I could gank someone as long as they had sums up or their mobility/cc, but I realized just coming to gank can burn something, or perhaps get a kill if they choose not to flash/die too quickly. Which is why if you see Zed just used W pre-6, and doesn't back up and he's a bit pushed up and doesn't see you approaching, that's a free flash or kill/both. That's another point, ganking. My brother doesn't like ganking, especially pre-6 on some champs like Eve, or others who don't have a gap closer or in some cases CC. You can still gank without ult or CC, which goes back to having vision control and awareness. Even if bot has tri and the other bush warded, if they're pushed up and with good communication, if bot initiates / baits as you get within vision, by then it's too late, as they might greed if one of your teammates is low, so not running away, or they might get cc'd as you come down, meaning they'll have to try and flash out or just die. Even so the threat of you there could be enough if they're low enough that they'd flash if your champ can potentially kill them (ex: Kass, Ori) even though pre-6 you can't really gap close without flashing and no hard-cc. Point being, ganking is vital, though I'm sure you know that (though I admit I used to afk farm and gank after 6 as well, simply because I didn't believe I could kill anyone without ult, though this is previous season me, like 4-5)
Pathing/jungle clear, understanding your champ/matchup of enemy jungler, and finally snowballing advantages all are dependant on on the champion in question, so for the champions you play, I'd advise looking up guides, forum posts, videos, most importantly players that play said champ (doesn't have to be a pro player) especially the one tricks. I used to play nunu a lot so I could tell you what works for me when I play him, but besides him I play Udyr, Rammus, Kha, and Hec (though this season only the first 2 + nunu as the other two I feel aren't very good ATM/not meta.) Nunu is definitely an obj. jungler, though ganking on him is hella easy and you should definitely go for early ganks, especially ones they don't expect.
Final notes, the jungler is a team player (unfortunately) sure depending on the champ you could 1v9 hard carry if you get yourself ahead, but from experience I've learned that you can't win on your own, even if you give them a solid early lead with first blood and good ganks resulting in double kills and drakes afterwords, but because they suck they throw that lead away by foolishly dying and being cocky and/or not knowing how to snowball the lead and letting the team catchup and eventually win a teamfight and run it down mid. That's from experience of recent games. Point is, if they don't suck like in my games, if you do that, they should be able to take that, and get more and more ahead, even if it's by small margins, which eventually result in a pick or fight that becomes a big margin, which becomes a win. Just ganking and applying pressure every so now but taking all the objectives when possible and denying the enemy it, as well as pressuring therefore getting towers either by splitting or forcing the enemy to back off, that is all good, because the aim of the game is to win after all.
Take everything I said with a grain of salt, as I'm no pro and I still have lots to learn myself, I'm not that good lol. I'd say I understand what needs to happen and what is good or bad, it's just the application in my games and doing it consistently isn't there yet. Plus I've been around long enough to know a thing or two, but it's still mostly from experience and from what I've looked up and learned from others either from watching or asking. Just watching PantsAreDragon and Trick2G play Udyr has helped me learn how to effectively apply Q dot, how to use stances during fights, management of passive, jungle clear, build order and how to build Udyr effectively, etc. So yea, imitation is key. If you want to be good, do what the good players do, don't forget you can change it up a little to your playstyle or what you like, obviously. Hopefully this helped, I'm writing this at 5:33 am so if I repeated something, oops. Feel free to hit me up if you wanna know more or ask me questions, at the very least I can share what works well for me and you can acknowledge it at best, assuming everything I've mentioned you already knew and/or isn't helpful lol.
