What's a person that orders something grand called? Like a customer or client but BIGGER

“Big spender” or “whale” are commonly used informal terms used.

At all company I worked for we had Tier 1 customers, Tier 2 customers, and Tier 3 customers. Tier 1 are the most important ones. "Tier 1 client" works fine too. Also called strategic accounts (i.e., their projects are big enough to warrant adjusting your company's strategy) or key accounts.  --- I just noticed you said "It could be a company itself, or a just a person, **or some employee at a company. The orderer**". That's a different concept. Do you mean the person who actually types up the order documents and sends them? I wouldn't normally refer to a person for that,  maybe like "the purchasing department of ABC corp".

That’s a complicated order.  Yes it’s still a client.

In video gaming, individuals who are willing to dish out tons of cash for the game are called whales. Whales are how many free to play games are funded. The term has been spreading to other industries, but it definitely is slang not professional terminology.

Pain in the ass client.

Client or customer would both be acceptable terms here. You could also say “VIP client” when communicating within your agency the importance of their order- but (at least in the uk) this term might come across as sycophantic if you used it with the customer themselves

That would still be called a client or customer. A person who sponsors an artist is called a patron/patroness, but that doesn't apply to your situation because the client is only hiring you for a specific job with a desired outcome as opposed to just giving you money to retain your skills. Patronage was much more common in Medieval times. In your first example, if someone hired you to design an apartment complex and had goals for you and wanted to be consulted on the design, they would be your client. However, if they gave you money and unlimited time and told you to make an apartment complex however you'd like, they would be your patron. Famous architect Frank Lloyd Wright sometimes worked this way. Wealthy people liked his work and just gave him money to go build them a Frank Lloyd Wright house.

more context is needed, but I would be more likely to modify the description of the job than the description of the client in this case. The words "customer" and "client" are mostly interchangeable, although client has more of a connotation of being a business and customer more of a connotation of being an individual person. But I wouldn’t typically describe a customer as “difficult” or “a pain in the ass" simply for placing an order that was inherently big or complicated – this is usually reserved for someone who is being particularly unreasonable/extra demanding. in your yogurt factory example, for instance, I would think that someone who orders 20,000 bottles is a “customer who had placed a large order.“ But if they want you to do it in half the normal time, or don’t like your normal yogurt and insist that you change the recipe or do other special things that you would not normally do, or change their mind a lot, that would make them “demanding “or “difficult“

Whale!

Client is what I would usually use, but there are a few alternatives and adjectives to make them stand out from "basic" clientele. Patron, Connoisseur, Distinguished Customer, VIP, High-end Client

Traditionally, someone who supported an artist by employing them would be a PATRON.

I know this may be unrelated, but this made me think a different word. Those who spend alot, the small individuals who account for a large portion of sales usually are called 'whales'. The term 'Whales' are mostly used for Free To Play games, which rely on micro transaction sales to maintain the business. E.g Genshin impact, mobile games

Could be “special client” or “VIP client”?

You might be looking for the term "VIP" - Very Important Person.

I’d still say client or customer, but I might qualify it by saying something like ‘high-profile client’ or ‘important customer’ or (internally) ‘high-value client’. If I was talking internally, like to a colleague, I might be more casual and describe them as a ‘big spender’.

Client is a broad word. It can be any individual or organization receiving a service. My wife’s patients as a nurse are technically her “clients” because she isn’t a doctor. My software support organization has an organization as a client, specifically a certain branch of an organization. And then there are million-dollar clients that are large organizations procuring a service from some other business, but they are all “clients”.

Client is fine. There is this show called suits and they use the term Client to refer to big corporate entities.

Those are clients. Great professional word. Here’s some slang when talking about “rich” clientele. “High roller” or “Whale” from casinos. Those crazy rich people who spend millions and get everything free (comped)? VIP- very important person. “High end” clientele… clients are all rich. If you say “this woman is very high end…” she’s rich and dressed like a rich woman. High end sales person- someone who works for a large “rich” label like Hermes Elite- very high class and expensive.

VIP client.

Customer or client is really it.. „account“ is also a business term that can be used interchangeably to say something like: ”XYZ Inc. just bought 1,000 cases of product. They’re by far our biggest client/customer/account.“

Client is fine.

Patron

I would probably say a demanding customer

a difficult customer, i suppose