The word "Die" is used very frequently in the preparation of dies and the press forming of products.
This word has the following meanings:

(1) Die ... Refers to the entire die. (Die)

In this case, the "die" is not used alone but is used along with a "mold". When used in this meaning, the word die is used after a word indicating its purpose of use. For example, a die can be called a "blanking" die. If the word "die" is used to refer to the entire die, many people may not understand it.
In addition, a "die" is used for forming shapes from plate-shaped or solid materials. These can be dies for press forming or dies for formation by forging.
When the word "die" is used to mean a "mold", it is used to refer to a die that prepares shapes from a molten material. These are molds used for injection molding or casting.
Therefore, use of the words "die" and "mold" is for referring to the entire die or mold
Also, a die can be made of metal, or can be made of sand (casting), or can be made of wood.

(2) Die ... When a die is separated into a top (upper) die and a bottom (lower) die, the word "die" in this case refers to the lower die. (Lower die)

Although it is very common to call this a bottom mold or a bottom die, sometimes it is merely called a "die". In this case, unless judgment is based on the context, a mistake can be made.

(3) Die ... This refers to a plate that constitutes the side in the die that receives the punch. (Die plate)

When people use the word "die" in spoken sentences such as "how is the die?", or "bring the die", or "the die is broken", etc., they mean the "die plate". Also, when used in expressions like "integrated die", or "insert type die", etc., the word "die" also refers to the "die plate".

(4) Die ... This refers to the shape of the punch receiving side of a plate that constitutes the punch receiving side. (Die)

There is no other expression other than "die" for expressing the side that receives the punch. The terms used in the work place may also be "the male die", "the female die", or the "millstone" (a drawing die), etc.
The word "die" refers to this part of a die in the expressions such as "die shape", "die radius", "the die is cracked", or "the polishing of the die", etc.

In daily usage, the term die only refers to the shape of the punch receiving side. Because this is difficult to understand, the word "die" is also used for referring to the plate or block constituting the die.
When you can correctly understand this word in its various forms of usage in conversations, then you can have confidence that you have understood press forming and dies quite well.