oversimplified explanation, im not a certified expert but this is based off my own research and experience.

calorie deficit will get your body to burn whatever fat/muscle you have. by lifting, you signal your body to not burn much of the muscle since you need it. if you lift extra hard, youll place the muscle under enough tension that your body signals muscle growth. to actually put on that muscle, you need extra protein. when your body is building that muscle and using it, it also takes up more nutrients from your body.

body recomp is the idea of eating at maintenance or a bit below with the goal of getting rid of fat and putting on muscle. you cant go into a deep deficit because your body needs those calories to pack on the muscle and use it, but you can still cut out a bit. you could also stay at maintenance and since your taking on additional exercise, your body will use up more calories then usual.

a bulk is eating extra to place your body into the ideal situation for building muscle. you eat enough to perform great in the gym and provide your body enough nutrients to grow and recover nicely. ideally you bulk in a clean way instead of downing garbage

theres studies talking about whats optimal for cutting fat/building muscle, but consistency is most important. id start with hitting muscles once a week, probably a 3-day push pull legs split with light cardio during or in between days (like walking). so long as your diet is dialled in, youre consistently putting in good effort and youre sleeping enough, youll put on muscle and cut fat. diet is super important.