If a particular fish can only be kept in a minimum 40 gallon tank, does that mean you can only house that fish?

The minimum tank size means that fish shouldn't go in a tank smaller than 40 gallons. That's all it means. So a fish with a minimum tank size of 40 gallons should not be placed in a 30 gallon aquarium.

So say I have a 30 gallon aquarium. I make sure that none of the fish have a minimum tank size exceeding 30 gallons. So I can keep, say, a Swordtail (whose minimum tank size is 30 gallons) in there with Praecox Rainbows (whose tank size is also 30 gallons) and with some Corycats (whose minimum tank size is 20 gallons). I can not, however, put in Boesemani Rainbows because their minimum tank size is 75 gallons, and 30 is less than 75 gallons. But if the minimum tank size is equal to or smaller than that of the fish meant to go into the tank, that's fine.

You also need to take into account if the fish you plan to keep together are compatible - which means that they will get along and live together well. Parts of being compatible is that they won't hurt each other, eat each other, out compete each other for food, frighten each other, etc. and also that they can all live in the same water parameters. Fish that won't do well together are incompatible.

The total amount of fish an aquarium can handle is called it's stocking capacity. If an aquarium is said to be fully stocked or close to max stocking, it means no more fish could fit in it. It depends on how much waste the aquarium can handle (the bioload capacity), how much territory the fish need, how active the fish are, and the group numbers of the fish. So you couldn't fit 20 Neon Tetras in a 10 gallon, even though 10 gallons is the minimum, because 20 Neons would produce way too much waste and be too overcrowded in a 10 gallon, and even though 10 is the minimum tank size 20 Neon Tetras in a 10 gallon would be over the max stocking, or overstocked. So the stocking level deals with the number of fish you can place into a tank. You can also overstock a tank by having 10 Neon Tetras and 8 White Clouds. Each fish has it's own bioload, how much waste it produces and how large it gets length and height wise being the biggest parts of that. Some fish have much higher bioloads than others. Goldfish are a good example of this. You could easily fit a dozen Neon Tetras in a 20 gallon - but a single Fancy Goldfish would fully stock a 20 gallon because it produces so much waste.

If you aren't sure about the bioload, you can try posting a question listing the size of the tank and the number and type of fish you have, and people with experience will be able to tell you if that is alright or not.

http://aqadvisor.com/ is a good resource to check things with and then double check on. A 75% stocked aquarium on there will allow for mistakes like overfeeding or missing the occasional weekly water change. A 100% stocked aquarium will not allow for any mistakes or the water quality will suffer.

The wording people will use when fish should not be kept with other fish is when they say the fish should be kept in a species only tank. A species tank will have just 1 type of fish in it, and it means for whatever reason (aggressiveness, extreme shyness, special needs) the fish isn't compatible with other types of fish, and does best either completely alone or with just others of it's own particular species. A good example of this is Dwarf Puffers, which are so aggressive they will attack just about any fish, and a fish large enough not to be hurt by them would also be large enough to swallow them.

technically no but it is highly advised. why? fish need space to grow and swim ontop of that bioload the more bioload you have the harder it is to keep the tank stable. I'm currently keeping an overstocked 55gal salt water aquarium and I am having issues dropping my nitrates. I possibly will eventually remove majority of the fish and then get it down where it needs to be and restock it. I could push my filtration in this tank more to help but it's already set up and it's hard to put in a sump. ontop of that everything practically is stable or lowering slowly except my nitrates so I'm thinking my nitrate kit is bad.

if the fish is small definetly doable but once it grows larger and larger you will eventually want to rehome to a bigger tank. space and bioload are particularly the issue I believe

usually not, it really depends on the fish though.

one betta rully stocks a 5 gallon.

one goldfish filly stocks a 20 gallon.

One oscar fully stocks a 75 gallon.

but somthing like a rainbow shark, or a pair of angels, ... that needs a 55 gallon, can be kept with other fish.