Die operations are often named after the specific type of die that performs the operation. For example a bending operation is performed by a bending die. Operations are not limited to one specific die as some Progressive die may incorporate multiple operation types:

Bending: The bending operation is the act of bending blanks at a predetermined angle. An example would be an "L" bracket which is a straight piece of metal bent at a 90° angle. The main difference between a forming operation and a bending operation is the bending operation creates a straight line bend (such as a corner in a box) as where a form operation may create a curved bend (such as the bottom of a drink can).
Blanking: A blanking die produces a flat piece of material by cutting the desired shape in one operation. The finish part is referred to as a blank. Generally a blanking die may only cut the outside contour of a part, often used for parts with no internal features.
Three benefits to die blanking are:
Accuracy. A properly sharpened die, with the correct amount of clearance between the punch and die, will produce a part that holds close dimensional tolerances in relationship to the parts edges.
Appearance. Since the part is blanked in one operation, the finish edges of the part produces a uniform appearance as opposed to varying degrees of burnishing from multiple operations.
Flatness. Due to the even compression of the blanking process, the end result is a flat part that may retain a specific level of flatness for additional manufacturing operations.
Broaching: The process of removing material through the use of multiple cutting teeth, with each tooth cutting behind the other. A broaching die is often used to remove material from parts that are too thick for shaving.
Bulging: A bulging die expands the closed end of tube through the use of two types of bulging dies. Similar to the way a chefs hat bulges out at the top from the cylindrical band around the chefs head.
Bulging fluid dies: Uses water or oil as a vehicle to expand the part.
Bulging rubber dies: Uses a rubber pad or block under pressure to move the wall of a workpiece.
Coining: is similar to forming with the main difference being that a coining die may form completely different features on either face of the blank, these features being transferred from the face of the punch or die respectively. The coining die and punch flow the metal by squeezing the blank within a confined area, instead of bending the blank. For example: an Olympic medal that was formed from a coining die may have a flat surface on the back and a raised feature on the front. If the medal was formed (or embossed), the surface on the back would be the reverse image of the front.
Compound operations: Compound dies perform multiple operations on the part. The compound operation is the act of implementing more than one operation during the press cycle.
Compound die: A type of die that has the die block (matrix) mounted on a punch plate with perforators in the upper die with the inner punch mounted in the lower die set. An inverted type of blanking die that punches upwards, leaving the part sitting on the lower punch (after being shed from the upper matrix on the press return stroke) instead of blanking the part through. A compound die allows the cutting of internal and external part features on a single press stroke.
Curling: The curling operation is used to roll the material into a curved shape. A door hinge is an example of a part created by a curling die.
Cut off: Cut off dies are used to cut off excess material from a finished end of a part or to cut off a predetermined length of material strip for additional operations.
Drawing: The drawing operation is very similar to the forming operation except that the drawing operation undergoes severe plastic deformation and the material of the part extends around the sides. A metal cup with a detailed feature at the bottom is an example of the difference between formed and drawn. The bottom of the cup was formed while the sides were drawn.
Extruding: Extruding is the act of severely deforming blanks of metal called slugs into finished parts such as an aluminum I-beam. Extrusion dies use extremely high pressure from the punch to squeeze the metal out into the desired form. The difference between cold forming and extrusion is extruded parts do not take shape of the punch.
Forming: Forming dies bend the blank along a curved surface. An example of a part that has been formed would be the positive end(+) of a AA battery.
Cold forming (cold heading): Cold forming is similar to extruding in that it squeezes the blank material but cold forming uses the punch and the die to create the desired form, extruding does not.
Roll forming: a continuous bending operation in which sheet or strip metal is gradually formed in tandem sets of rollers until the desired cross-sectional configuration is obtained. Roll forming is ideal for producing parts with long lengths or in large quantities.
Horning: A horning die provides an arbor or horn which the parts are place for secondary operations.
Hydroforming: Forming of tubular part from simpler tubes with high water pressure.
Pancake die: A Pancake die is a simple type of manufacturing die that performs blanking and/or piercing. While many dies perform complex procedures simultaneously, a pancake die may only perform one simple procedure with the finished product being removed by hand.
Piercing: The piercing operation is used to pierce holes in stampings.
Progressive die: Progressive dies provide different stations for operations to be performed. A common practice is to move the material through the die so it is progressively modified at each station until the final operation ejects a finished part.
Shaving: The shaving operation removes a small amount of material from the edges of the part to improve the edges finish or part accuracy. (Compare to Trimming).
Side cam die: Side cams transform vertical motion from the press ram into horizontal or angular motion.
Sub press operation: Sub-press dies blank and/or form small watch, clock, and instrument parts.
Swaging: Swaging (necking) is the process of "necking down" a feature on a part. Swaging is the opposite of bulging as it reduces the size of the part. The end of a shell casing that captures the bullet is an example of swaging.
Trimming: Trimming dies cut away excess or unwanted irregular features from a part, they are usually the last operation performed.
what do you call upper part of die and lower part of die..?
The lower part of a die is called a bolster