No, what you were told about home improvement stores carrying lesser quality tile simply isn't true.
Here's what you need to know:
Every ceramic tile manufacturer will get his clay and paints from other manufacturers, and so the ceramic tile manufacturer has no control over changes made to his feedstock by his suppliers.
So, if you're a company that makes ceramic tiles, and the company you're buying your glazing paints from buys their red pigment from a chemical distributor in their town, and that distributor finds out that the red pigment he's buying from BASF is going up in price, so he starts buying red pigment from Sun Chemical instead, then that change COULD affect you. That's cuz if you start using a red glazing paint on your tiles that uses a different pigment, you could end up with a perceptibly different colour. Even baking the tiles in a kiln at a different temperature or for longer or shorter or with different humidity could affect the tiles in some way so that one batch is slightly different than another batch of tiles.
To manage this situation, what tile manufacturers do is assign each batch of tiles they make a "dye lot number". Every tile with the same dye lot number was made with the same clay, the same glazing paints, baked in the same kilns at the same temperature and cooled in exactly the same fashion, so they should all be identical. The same dye lot number on two boxes of tile is your guarantee that two boxes of tiles come from the same batch of tiles, and therefore should be identical in every respect.
How do you know which number printed on a box is the dye lot number? Except perhaps for the manufacturer's name, the dye lot number will be printed with the largest font you see on the box of tiles. They do that so that the warehouse personnel can see what stock they have without having to get on a fork lift and use it as an elevator to inspect the boxes closely, which would be a pain. They print the dye lot numbers on the boxes of tiles large enough so that you can read the dye lot number off the box even if it's on a shelf 20 feet off the ground.
Typically, a dye lot number might be something like "AZ1K9". That doesn't mean anything at all. The dye lot number itself has no meaning whatsoever. Just as long as every box of tile you buy has that same dye lot number printed on it, then every tile in every box should be identical in every respect.
When you order tiles from a ceramic tile store, they understand the significance of dye lot numbers, so if you order 150 square feet of ceramic tile from them, they will send the order to their wholesaler, and the guys at the wholesaler will fill each order with tiles from the same dye lot.
But, the people working at home improvement stores aren't so knowledgeable. They will simply order 10,000 square feet of a certain manufacturer's style and colour of tile. For example, 10,000 square feet of San Lorenzo (manufacturer) Lago (style) in Mist Green (colour).
In a case like that, the wholesaler says to the home improvement store: "We don't have that much in a single dye lot. Is it OK if we make up that order from different dye lots?" and the people at the home improvement store say "Sure". So, the wholesaler sends off tile from different dye lots to meet the order.
Then, when the tile comes to the home center, the people working there wouldn't know a dye lot number if it bit them. They just put out the boxes willy nilly, and you might get the same tiles from 4 or 5 different dye lots for their customers to choose from. The customers don't know about dye lots either, and they end up buying boxes of tiles from several different dye lots.
So, the tile you typically see at home centers is as good quality as the tile you'd order from a tile or flooring retailer, it's just that it's all from different dye lots, and there COULD be differences in the tiles from one dye lot to another.
In a perfect world, the people working in the home center SHOULD only put tiles from ONE dye lot out for sale until they start to run out of that dye lot, then put another out, and so on. That way, people will get tiles from the same dye lot. And, then, put all the small quantities remaining from different dye lots out on sale for a reduced price (perhaps their cost price). But, the world isn't perfect and Lassie kills chickens, and we have to deal with the fact that the store employees don't always know as much as we'd like them to know.
So, it's typically not that much of a problem, but if you know what dye lot numbers are, you can know whether or not there's the possibility that the tiles in the boxes are gonna be identical, or if there's a good possibility they won't be. If you're at least aware that they might not be, then you can take corrective action. If there's a perceptable difference in the tiles between different dye lots, you can mix up all your tiles in advance so that the whole wall or floor has slight varying colours from tile to tile to make a "pattern" of sorts using that colour variation. Or, you can use the tile from one dye lot on one bathroom wall, and those from another on a different wall. Or, you can return the tiles from one dye lot and buy more of the other so they're all the same. At least you're aware of the situation and can take steps to deal with it.
If you don't do that, then you can end up tiling a wall or floor, and after all that hard work, you step back and notice that the tiles on one side of the wall or floor are very similar in colour to those on the other side of the wall or floor. And, that's not exactly a "rewarding" feeling.
So, the tiles Home Depot or Lowes sells aren't lesser quality, but there is the greater possibility of a newbie running into problems with tiles not "looking" the same using tiles from a home center than from a tile or flooring retailer, and it's entirely because everyone in one distribution stream knows and understands what dye lot number are, whereas no one in the other distribution stream does. But, if after reading this post, if every box of tiles you buy from Lowes or Home Depot all have the same dye lot number on the box, then you won't have any fewer or more problems installing them than if you'd paid extra and bought your tiles from Le Chic Ceramique Boutique.
Now, Porcelain floor tiles will be given a "hardness rating" from one to five diamonds, 5 diamonds being the hardest, but if you see the same tile for sale in Home Depot and in a flooring store, there won't be any difference in quality between them. Both will be equally hard.
And, porcelain floor tiles differ from ceramic floor tiles, the former being harder and being homogeneous throughout it's whole thickness, so that if you drop a knife and chip a porcelain floor tile, there's no colour difference to make the chip stand out. Ceramic floor tiles will just have a coating baked onto their top surface, so that if you chip a tile by dropping a knife on it, the clay biscuit of the tile will be a different colour, making the chip stand out.
Ceramic wall tiles will vary in both the kind of clay "biscuit" they have (which is the clay body of the tile) and it's thickness. Better quality tiles (in my view) have a good 3/16 inch thick white clay or red clay biscuit, and you want a thick strong clay biscuit that can stand up to an accidental smack from a glass bottle of hair shampoo (or whatever) without cracking. There are some wall tiles out there that are thin as potato chips and about as strong, and you want to stay away from them.
Some people say that the white clay tiles are stronger than red clay. I've used both and my personal experience is that there isn't much difference in strength, but if I had to say which was stronger, I'd say the red clay is a bit stronger than the white clay. What's most important is the thickness of the clay biscuit, not what colour it is.
Finally, EVERY kind of tile will have dye lot numbers, not just ceramic tiles. Vinyl composition floor tiles will also come in boxes with different dye lot numbers. Ditto for Peel & Stick, I think.
That's really about all you need to know about buying tiles.