It really depends...
Minimum Order Quantities(MOQ) are largely determined by what materials you use. When dealing with smaller scale manufacturing, purchasing stock materials will help reduce your MOQs, but you also have to live with the constraints of stock materials - namely your choices will be limited.
Surcharges can be common
Fabric is typically the biggest reason why the minimums vary so much. If the fabric is sourced from a stock supplier, the minimums will be smaller. But you'll also have to deal with the risk of the fabric not always being in stock. That's why established brands take the time to develop long term relationships with mills and typically mill their own fabric. This not only improves quality, it also helps increase predictability. Many fabric companies will also include a surcharge if the order quantity is below a set amount.
Specialty materials and specialty processes can also increase MOQs. The industry is constantly introducing new technologies, however the latest and greatest technology is also very expensive. This means factories have to have higher minimums to make sure their orders can cover the cost of the new technology. Heat transferring cloth onto cloth is a good example. The minimums have declined over the years, but when it first began 100,000 piece minimums were common.