Consider how latency and bandwidth works with hard-copies carried by foot.
Say you have a boxful of hard copies—about as much as you can carry without being significantly slowed down by the weight, and two places you might want to bring it, one 50 m away and one .5 km away.
Let's say you walk at about 5km/h. It would take you 1.2 minutes to bring the box to the first place and return, and 12 minutes to bring the box to the second place and return.
Now lets say you have to bring 100 boxes. You'd have to make 100 trips, so your total time carrying would be 2hours and 200hours respectively.
Now, let's make these things better.
Let's say you enlist 99 helpers. You can now have more bandwidth. You can now bring the 100 boxes in 1.2 and 12 minutes respectively.
Let's say you enlist 2000 helpers. You now have even more bandwidth. You can now bring the 10 boxes in 1.2 and 12 minutes respectively. The extra bandwidth hasn't helped because you've maxed it out, and the latency is the same.
Let's say you get rid of the 99 helpers, but buy a bicycle, and you can do a healthy 40km/h on it. You can now do the one-box trips in 9 seconds and 1.5 minutes respectively. You now have less latency. The 100-box trips will take 150 minutes and 25hours though.
Now, obviously the bicycle (lower latency, some extra bandwidth) is better at bringing one box of papers quickly, while the massive team of helpers (same latency, much more bandwidht) is better at bringing lots of boxes.
Network connections compare with each other in ways similar to how these different means of transporting hard copies compare.
Downloading a very large file is akin to the task of transporting lots of boxes, and so the more bandwidth, the better.
Playing a game tends to involve lots of small messages, so it's like the task of carrying one box over and over (we can't bulk-transport all the boxes, as the next box isn't ready yet). The lower the latency, the better.
But in our analogy, there's no reason why we can't have a massive team of helpers who all have bicycles.
And extend the analogy, different network connections will differ not only in latency (foot vs bicycle) and bandwidth (how many helpers) but also in having different short-cuts available, and different points they have to go through, so one may be lower latency for one trip and higher for another.
But where the analogy is accurate is that while we can have two connections where one is better by one metric and worse by another, we can also have two connections where one is better than the other by both measures.