[peabody]

There are several types of missions, but answer the specific questions asked.

The two basic patrol/sink missions are "Reach Zone" and "Patrol Area", the icons are different for each one. Patrol has the binoculars and Reach zone has a flag unless it was changed by mods. You will not see the specific wording of "Reach Zone" it is used by the Mission Editor.

On a "Reach Zone" you only have to get to the star and it turns grey, complete, and then you are usually given a second objective to sink enemy vessels.

In the Patrol Area mission, it is not enough to just reach a certain location, you must 'patrol' the area for whatever amount of time is set by the person that wrote the mission. And as mentioned, you need to stay in the 'patrol area' for the mission to complete. I always felt it was a good idea to put the area size and amount of time in the orders so you know what it is, but not everyone does that.
As for leaving the zone, most are written so that if you leave the zone the time starts over, (continuous) but can be written so you can leave the zone and reenter to complete the mission (non-continuous). Example: If it is continous for 48 hours you must stay in the zone for 48 hours without leaving. If it is non continuous, you can patrol the zone for 20 hours then leave to attack a convoy, return to the zone and in 28 more hours it will complete
NOTE: I never actually tested the non continuous to see if it actually works or not.

As for ships not counting, the mission can be set to sink tonnage and will complete or not depending on the amount of tonnage set AND the type of Tonnage set in the editor.
The types are:
Any
Merchant
WarShip
Merchant Replenesment
Merchant Cargo
Merchant Tanker
Merchant Troop Transport
Warship Capital
Warship Escort

So whether the mission completes or not depends on how it is written. If it is written to sink 10,000 tons of merchants shipping then sinking a warship will not count toward finishing the mission, but you WILL get credit (renown) for sinking it. If the mission orders say to sink merchant shipping but the type is set to "Any" then warships will count toward the total tonnage. (in other words, the mission was not written correctly and will work but not the way it was intended to work)

The only type of mission that requires you to stay in a zone for them to count is "Destroy Enemy Class" which will be a specific Class of ship such as Fuso Battleship and will be set that way, but normally isn't used because it is very specific because it must be a certain ship in a certain location and doesn't work well with the SH4 Random style of doing things. I do not think it is used in the stock game at all but may very well be used in the more historical MODs.

I hope some of that makes sense.