New2grammar wrote:

Is there any difference between a fish tank and a aquarium in terms of cost, size and etc?

noun:   a tank or pool or bowl filled with water for keeping live fish and underwater animals

I believe the above definitions will be helpful..

The first definition of aquarium has the same meaning as fish tank, am I right?

Basically, yes.  In many situations they could be used interchangeably  -- I might ask my daughter if she had cleaned the aquarium lately, or I might say the fish tank.  But "aquarium" has a more expensive, decorative implication -- "fish tank" is more basic.   The phrase "My, what a beautiful _______________" should be completed with "aquarium" rather than "fish tank." 

For example,  a Chinese restaurant I go to has a beautiful aquarium in the front of the restaurant for people to look at while waiting for a table.  Near the kitchen, they have a tank of live lobsters waiting to become someone's dinner.  I don't know if restaurants ever keep life fish to be turning into dinner, but if they did, they would probably call the place they keep them a fish tank, not an aquarium. 

Hi New2grammar,

Typically, a fish tank is something smaller, say,  5-10 gallons capacity which most of us have in our house.  If you say “ I have an aquarium in my house”, the impression I have is that of a large and elaborately decorated fish tank with a large selection of expensive, and often exotic tropical species with seascape in aqua color lighting.

No one in their normal mental capacity will call the Monterey Aquarium a fish tank in my opinion, although he may call his 10 gal fish tank an aquarium.