Welcome to the forum!
Let me start with some quick and good news: the culture mix you have is perfectly fine to use for a wide variety of cheeses. Depending on the proportions of meso to thermo, the mix may or may not work as well for some of the Italian/Swiss types of cheese, but it would be a very good choice for cheddar, Gouda, "baby swiss," blue cheeses, and many others. You could even use it for camembert/brie. Both cultures are naturally present in raw milk, so if you are using raw milk, even if you add a meso culture to make sure it dominates, you will also have some thermo, and vice versa.
Now for the lengthy explanation:
While there might be some truth to the distinction you have made between meso and thermo cultures, it is really not a reliable rule. Mesophilic cultures do tend to be used for many softer cheeses, including camembert/brie, but they are also used for hard cheeses such as cheddar and semi-hard such as Gouda. Meanwhile, thermophilic cultures are used for the harder Italian/Swiss types of cheese, including Parmesans, but thermo is also the culture that is typically used to make mozzarella - a very soft cheese. And sometimes people use thermo to make camembert/brie for a slower-ripening product.
Both cultures will thrive in the 90-100°F (32-38°C) range that is typically used to ripen the milk before adding rennet. After the curd is set and cut into cubes, more heat may be added, depending on the type of cheese desired; mesophilic can survive up to 105°F (40-41°C), but above that temperature, it will start to die. Thermophilic can survive up to 120°F (49°C) or higher.
How hard the cheese is depends on a number of factors, but especially important is the amount of fat and moisture in the curd. Moisture is controlled primarily by four factors: the length of time the cheese is allowed to coagulate (after adding rennet); the size of cubes into which the curds are cut after coagulation; the amount of cooking of the curds after cutting; the amount of stirring of the curds after cutting. The fact that thermophilic cultures can withstand higher heat, which translates to a drier curd, is what leads to the connection between thermophilic culture and hard cheese - but really it is not so much the culture as it is the way the curd is processed.
In one sense, both cultures do the same thing: they consume the lactose in the milk and convert it to lactic acid. The acidity, along with drying and salting, is part of what helps to preserve cheese; the pH level at different stages of the process also has a significant effect on the resulting texture - lower pH (higher acidity) at draining, for example, will remove some of the calcium, changing the strength of the chemical bonds in the cheese.
n my experience - not an expert by any means, but an experienced amateur (I've made about 100 cheeses) - I would say that, all else being equal (i.e., same amount of moisture, fat, and pH level), the mesophilic cultures are more likely to give a crumbly result, and the thermos more likely to give a smooth and flexible result; mesophilic is more likely to give buttery / cheddary flavors, and thermophilic is more likely to give nutty flavors. But again, so much depends not just on the culture, but on the process!
A marvelous book that helps to explain the processes at work is Mastering Artisan Cheesemaking by Gianaclis Caldwell - highly recommended. It gives a solid understanding of the underlying processes without getting too technical.
The other marvelous resource is this forum - we are always glad to offer recipe ideas, help diagnose problems, commiserate over setbacks, and celebrate success!