We know there are several common types in R, such as, vector, list, matrix, and data.frame.
Here I’m going to see these 4 types more details.

1. What are the differences between vector, list, matrix, and data.frame?
2. What are the outputs of is.atomic() and is.vector()?
3. What are the outputs of typeof()?

1. What are the differences between vector, list, matrix, and data.frame?

We can seperate these four types to two groups from different aspects.

(a) Elements type aspect

• Homogeneous data: vector, matrix
• Heterogeneous data: list, data.frame

Which means all elements in vector and matrix have to be the same type (integer, double, or character ect.). But elements in list and data.frame can be different types.

For example:
Vector has same type of elements

# vector
v <- 1:4
#  v
# [1] 1 2 3 4

v_ch <- c("a", "b", "c")
# v_ch
# [1] "a" "b" "c"

What if we give a vector different type of elements?

v <- c(1, "2")
# v
#[1] "1" "2"

As you can see, R forces 1 to be character.

But what is the priority? Why not “2” become numeric?

Because the hierarchy for coercion is:

• logical < integer < numeric < character

So this is why numeric would be force to character.

reference

(b) Dimension aspect

• 1 Dimension: vector, list
• 2 Dimensions: matrix, data.frame

2. What are the outputs of is.atomic() and is.vector()?

Let’s see the outputs of these four types.

v <- 1:4 # vector
l <- list(1:4) # list
mat <- matrix(1:2, ncol = 2) # matrix
df <- data.frame(a = 1, b = 2) # data.frame

(a) is.atomic()

# > is.atomic(v)
# [1] TRUE
# > is.atomic(l)
# [1] FALSE
# > is.atomic(mat)
# [1] TRUE
# > is.atomic(df)
# [1] FALSE

As you can see the results, is.atomic() gives boolean values.
And the output is to see if the object is Homogeneous data or Hetergeneous data.
Hence, vector and matrix get TRUE, list and data.frame get FALSE.

(b) is.vector()

# is.vector(v)
# [1] TRUE
# is.vector(l)
# [1] TRUE
# is.vector(mat)
# [1] FALSE
# is.vector(df)
# [1] FALSE

In contrast with is.atomic(), is.vector() checks from Dimension aspect.

3. What are the outputs of typeof()

# vector
v <- 1:4  # all elements are numeric
v_ch <- c("a", "b", "c")  # all elements are characters
# list
l <- list(1:4)  # all elements are numeric
l_ch <- list(a = "a", b = "b") # all elements are characters
# matrix
mat <- matrix(1:2, ncol = 2)  # all elements are numeric
mat_ch <- matrix(c("a", "b"), ncol = 2)  # all elements are characters
# data.frame
df <- data.frame(a = 1, b = 2)

Let’s see the results,

# ---vector-------------
# > typeof(v)
# [1] "integer"
# > typeof(v_ch)
# [1] "character"
# ---list-------------
# > typeof(l)
# [1] "list"
# > typeof(l_ch)
# [1] "list"
# ---matrix-------------
# > typeof(mat)
# [1] "integer"
# > typeof(mat_ch)
# [1] "character"
# ---data.frame-------------
# > typeof(df)
# [1] "list"

From the result of ouputs, we can see it checks if the object is Homogeneous data or not.
If it is Homogeneous data then typeof() will show the type of elements.
But if the object is Hetergeneous data, it will give only list as output result.

More detail about Data Structure can be found here

Reference:
R深入|数据类型