Ok I hope this helps explain some things a little.
There are structural changes with strength training and neural changes.
Structural changes provides greater muscle fiber size (and more collagen fibers etc) to contract so with a greater cross sectional area you can get more force from that muscle.
Neural changes involve enhancing the amount of muscle fibers you can use at one time and the amount of force that these fibers can generate.
Now this is really basic and I wont go into it much but to get stronger you need to increase both of them, depending on some peoples sports, hypertrophy isnt worthwhile due to weight classes etc so they work more on the neural side while bodybuilders want size so they go for more of the structural work. If you just wanting to get stronger and a bit bigger then finding a balance would be a good idea.
To get structural changes you usually need a good deal of volume that creates “damage” and you body repairs/replaces these fibers and you get bigger. To get neural changes most training (other ways but this the most basic and most used method) involves high force components 1-3 reps with lower volume.
So look to add both of these elements to the mix, maybe swapping and changing every few weeks, or incoporating both modes into each training session or making one session a week more high force and one more repetitive etc etc etc.
Hope that helps your understanding. You can get a LOT stronger than you are without adding any appreciable muscle mass i.e. I went from a 90kg deadlift when i started to a 150kg deadlift weighing about 2-3kgs more at the same bodyfat %. You can keep hammering your body with similar weights and your size will increase yet dont expect this to continue for very long at all as you will plateau.
If you want to get bigger slowly dont eat too much more than you bmr and activity levels and it will slowly progress try between 250-500 calories extra each day and reassess your goals as you go along (getting to much body fat then you decrease the calorie intake etc etc)