Re: Definition of 'Fit' ?
I was in a similar position when i first started. Thought i was fit until i started boxing. You probably have developed reasonable muscular endurance. However if your gassing on boxing related exercises in rounds such as pads ect then i would suggest you train anaerobic system. Sprints and intervals. Or better yet if you are suffering specifically on pads.... do more pads!
Its easy to talk about our strengths and focus on that and not our weakness's
For example i was shit at sprints and interval training but did alot of long distance, took me a while to accept i was doing things wrong and running 6 -8 miles a day wasnt helping me. So changed it up with intervals and not looked back since. I also couldnt do more than 5 chin ups, decided they wern't that important as i could do loads of push ups. Once again realised i was wrong, i can now knock out 25 chin ups.
Anyway blabbing now .. work on your weak points and you will get all round fitness