What is the proper way to address NCOs in different branches?

In the Marine corps it's their full rank. sergeant. Staff sergeant. Gunnery sergeantetc.

In the Navy it is Chief, Sr. Chief, and Master Chief!! It's the way I was taught!!

In the Marine Corps we have a rank structure that we all adhere to. E-1 to E-3, are referred to as Privates, PFC's and Lance Corporals with their last names. E-4 & E-5 are called Non-Commissioned Officers and are referred to as Corporals and Sergeants. The E-6 through E-9's are referred to as Staff Non-Commissioned Officers and Senior Non-Commissioned Officers. Our E-6's are called Staff Sergeant, E-7's are Gunnery Sregeants, hence the name Gunny, the E-8's are either First Sergeants or Master Sergeants, depending upon what the individual chooses when eligible to be selected for the next rank. E-9's is our Senior rank, which they can either be a Sergeant Major or a Masrter Gunnery Sergeant. Both the First Sergeant and Sergeant Major are the Senior rank and they are administrative in general. The Master Sergeant and the Master Gunnery Sergeant are Technical MOS's in their field of expertise. Both th E-8's and E-9's are considered to be our Senior Staff NCO's. But the most senior rank is our Sergeant Major of the Marine Corps. He is the Senior enlisted Marine who advises our Marine Corps Commandant General Robert Nellore. He out ranks all Enlisted personnel in the Marine Corps. I should know because I came up through the ranks from Private to Gunnery Sergeant before being selected as Warrant Officer 1, I retired as Chief Warrant Officer 3 after serving 21 plus years in the Marine Corps in 1994 and still serving our Country. Hopefully this would give you and insight of what we Marines, Past, Present and Future understand how important our rank structure is to us all.

Semper Fidelis,

Gunner K.

In the Navy it is Chief, Sr. Chief, or Master Chief!! Been Chief for over 100 years!! We are a proud group of men and women!! Our E4 to E-6's are addressed as Petty Officer!!

By their rank. That is always the proper way. Sergeant, Master Sergeant, Corporal, Petty Officer, Chief.

Calling a Marine SGT., Gunny, SGM ect Sir will get the same response I gave when I have been called Sir " Don't call me Sir I work for a living" LOL

First of all learn the different grades and insignia of all the services, this should be taught in basic training.
When assigned to a Joint Command I was appalled at the number of long time service members, both Officers and NCO's who didn't know the grade systems.

In your scenario Gunny works or Gunnery Sergeant. I never met a Gunny that got uptight about being referred to as one. Enlisted are referred to as last name, rank, or Marine. Corporal, Sergeant and Staff Sergeant as rank and last name or just rank but never "Staff" for a SSgt unless you enjoy filling sand bags or burning shitters. Unlike the Army it's not wise to refer to any enlisted above Gunny as Top. I think that's how 1st Sgts are often referred to in Army and it is a term of respect as they are the Top Sergeant, or at least used to be when there were only 7 enlisted paygrades. I heard my oldest brother in Hawk Missiles in 70's at Key West use the term First Shirt a few times also. Try Top with a Master Sergeant USMC and stand by for heavy rolls. Some don't sweat it and it depends on the unit and individuals concerned. If it is the wrong guy it will likely be met with a comment like "do I look like a top, why don't you try to spin me a few times?". First Sergeants are referred to as one. Sgts Maj and MGySgts are referred to as just that except MGySgts are often called Master Guns or Master Gunny. You may have witnessed some "boots" fresh out of boot camp. Recruits first and last word out of their mouth are Sir or Ma'am and it takes awhile to get out of that habit. Folks checking into their school or first duty station are often locked up at attention and might address the Asst Duty NCO in boot camp fashion. In boot camp they might say "Sir, this recruit requests permission to speak with the Drill Instructor, Sir". Likewise a boot might report in to school or duty station at attention and address a LCpl as "Sir, Private Smuckatelli is reporting as ordered, Sir" - while at attention, staring at the bulkhead and extending his/her orders in hand. It's comical to watch but they quickly figure it out.

Marine Corps Boot Camp, they are called recruits. As for our Drill Instructors, the recruits are taught to address their D.I.'s. as Sirs or Ma'am. Once the recruit passes all three phases of their training, then they are given the Marine Corps Eagle, Globe, and Anchor because of the rites of passage. You who once was a Marine or currently serving as a Marine would understand what I just said.

We had a master Chief (E-9) who once said, "Don't call me sir, my parents were married"