Available on the market or in the market, which is correct?

I would use "on the market" when talking about whether something can be generally bought or not. Example: "Samsung have a new phone available but it's not on the market yet." "In the market" is most often used about someone who is hoping to buy something. Example: "I have a number of guitars but I'm always in the market for a nice Martin D25" If one is referring to a specific place (e.g. the market place of a town, which would be referred to locally as 'the Market'), you might say that a trader 'has a stall on the Market' (meaning that he sells things from a stall there) but you would tend to use 'in' when referring to the marketplace as a location: "Where is Daisy?" "I'm not sure but I think you'll find her in the Market" [as opposed to somewhere else].

Grammar is confusing. I hate it. :))

I think you are correct in your understanding.

I also would say "on the market" and I agree with your definition.