SOmetimes, they're different, sometimes, they're not. If the part numbers are identical, they're likely identical. IF they have different numbers or letters (like a dash x, for example), they're different.
SOme have said that on some examples, those sold at the big box stores may come off of the same assembly line, but do not go through the same quality control steps...making the buyer the QA person that may not know what to look for. This lets more 'pass', so they can be sold cheaper.
Keep in mind that low-flow toilets still need to change all of the water in the bowl with a flush. The less water they use, the less there can be in the bowl or you're left with a less than clean mix...
There is only one 'right' bowl water height. Generally, there's nothing you can do to raise it. TO check that it's at the max, note the water height - maybe mark it with something, then SLOWLY pour some water into the bowl. If it rises, and STAYS higher, it's not adjusted properly, and yes, you can raise it a bit. If it stabilizes back where it was, there's nothing you can do.
To get a deeper level, you need a differently shaped bowl, but then, it wouldn't be as wide. Gone are the days when you can buy a toilet that flushes as much as 7-8 gallons - those had huge, deep bowls and monster tanks.