And then you go punching a heavy bag with light gloves. Maybe throw hooks, some uppercuts, whatever. That right there is not strength training.
I don't use gloves to punch heavy bags unless my knuckles start to bruise, then I'll put on light gloves to protect my knuckles for a little longer.
I use 10 pound weights around my wrists to train my long guard and at the same time do footwork in at 3 levels. I start off with a high stance and finish up in low stance. The 10 pound weights around my wrist help to build the muscles involved with holding my guard up. Ideally I would use this if I'm going to do any punches as it allows the weight to move as I punch instead of sitting on the end of my wrist.
I also use an 8lb slam ball to train my grip and arm strength while doing specific tiger techniques. When I train my staff, I use a heavier staff and do grip training exercises that are specific to the use of the staff. If I was training kali, then I would probably invest in a bian for strength training and go through some of my techniques using the bian.
That right there is not strength training. It's you working on technique and getting a good cardio workout, but unless you're some kind of super newbie who will get stimulated by any form of physical activity, the only way to build pure strength and muscle bulk is to eat lots of protein/calories and lift heavy.
When I hit the heavy bag I work on the following things.
1. Core strength building because my core is powering my punch which means I need continue to turn my core into the bag and not just stop. This works and strengthens my waist.
2. Impact conditioning this help conditions my arm, tendons, and ligaments, joint, and knuckles so that when I strike the bag, I'm not damaging those areas. Lots of guys who lift weights in the gym cannot hit the heavy bag like I can. If I hit the heavy bag soft, then I'm working on conditioning. If I hit it with 50% power then I'm working on technique. If I'm hitting it at 100% power then I'm working on power and technique.
3. I don't get cardio from the heavy bag. I don't need the heavy bag to train cardio. I do footwork drills, forms, and kung fu shadow boxing for cardio. My own opinion is that heavy bags aren't good for cardio. It's good for other things but not for cardio. Bags and grappling dummies are good for strength building in this manner.
This type of training makes it easier throw people, because I strengthen the muscles.
Here's a clip from one of my workout sessions during the summer. Staff training with rings. Then 130 squats with a 20lb weight. This both exercises strengthens the legs and arms. Both are part of my martial arts training. The staff with weights also keeps the technique
None of the exercises I do will make me bigger. They will make me stronger but I'm not going to gain a lot of muscle mass. I'm not going to look like a body builder from doing these types of exercises but I will be stronger.