diff --git a/toolchain/docs/check.md b/toolchain/docs/check.md
index ecb6ee0a8e609..c037e0498ac4e 100644
--- a/toolchain/docs/check.md
+++ b/toolchain/docs/check.md
@@ -84,17 +84,18 @@ instruction, as described in
 [sem_ir/typed_insts.h](/toolchain/sem_ir/typed_insts.h) (also see
 [adding features for Check](adding_features.md#check)):
 
+-   An `InstKind kind;` member if the instruction has a `Kinds` constant making
+    it a shorthand for multiple individual instructions.
+
 -   A `SemIR::TypeId type_id;` member that describes the type of the instruction
     is present on all instructions that produce a value. This includes namespace
     instructions, which are modeled as producing a value of "namespace" type,
     even though they can't be used as a first-class value in Carbon expressions.
 
--   Up to two additional, kind-specific members, which are typically ids or
-    indexes derived from `IdBase`. For example `SemIR::Assign` has members
-    `InstId lhs_id` and `InstId rhs_id`. And `SemIR::ClassElementAccess` has an
-    `ElementIndex` into the fields of the class to define which field it is
-    accessing. See the comment in
-    [sem_ir/typed_insts.h](/toolchain/sem_ir/typed_insts.h) for more details.
+-   Up to two additional [kind-specific members](#instruction-operands). For
+    example `SemIR::Assign` has members `InstId lhs_id` and `InstId rhs_id`. And
+    `SemIR::ClassElementAccess` has an `ElementIndex` into the fields of the
+    class to define which field it is accessing.
 
 Instructions are stored as type-erased `SemIR::Inst` objects, which store the
 instruction kind and the (up to) four fields described above. This balances the
@@ -102,21 +103,23 @@ size of `SemIR::Inst` against the overhead of indirection. All instructions have
 with them a `LocId` that tracks their source location, and is stored separately
 on the `InstStore` and retrieved by `GetLocId()`.
 
-A `SemIR::InstBlock` can represent a code block. However, it can also be created
-when a series of instructions needs to be closely associated, such as a
-parameter list.
+A `SemIR::InstBlockId`, used to index into `SemIR::InstBlockStore`, can
+represent a code block. However, it can also be created when a series of
+instructions needs to be closely associated, such as a parameter list.
 
-A `SemIR::Builtin` represents a language built-in, such as the unconstrained
-facet type `type`. We will also have built-in functions which would need to form
-the implementation of some library types, such as `i32`. Built-ins are in a
-stable index across `SemIR` instances.
+A number of instruction types in
+[sem_ir/typed_insts.h](/toolchain/sem_ir/typed_insts.h) are builtin
+instructions, such as `SemIR::TypeType` which represents the unconstrained facet
+type `type`. We will also have built-in functions which would need to form the
+implementation of some library types, such as `i32`. Built-ins have stable ids
+in the `SemIR::InstStore` across `SemIR` instances.
 
 ### Instruction operands
 
 The kind-specific members on a typed instruction struct can be of any type
 listed in the `SemIR::IdKind` enumeration defined in
-[sem_ir/id_kind.h](/toolchain/sem_ir/id_kind.h). The most commonly used kinds
-refer to other instructions:
+[sem_ir/id_kind.h](/toolchain/sem_ir/id_kind.h), typically derived from
+`IdBase`. The most commonly used kinds refer to other instructions:
 
 -   `SemIR::InstId`: Refers to a specific instance of an instruction. For
     example, this should be used if the operand may have side-effects or a
@@ -134,11 +137,11 @@ documentation for the ID type for more details.
 
 ### Parameters and arguments
 
-Parameters and arguments will be stored as two `SemIR::InstBlock`s each. The
-first will contain the full IR, while the second will contain references to the
-last instruction for each parameter or argument. The references block will have
-a size equal to the number of parameters or arguments, allowing for quick size
-comparisons and indexed access.
+Parameters and arguments will be stored as two blocks (referred to by
+`SemIR::InstBlockId`) each. The first will contain the full IR, while the second
+will contain references to the last instruction for each parameter or argument.
+The references block will have a size equal to the number of parameters or
+arguments, allowing for quick size comparisons and indexed access.
 
 ## SemIR textual format