Single digits seem to be greater than double digits

[DeaD_EyE]

Please use the

[python][/python]

tags to wrap your code. Otherwise the indentation is lost and syntax highlighting does not work.

print("hello world!")
print("What is your name?")
name = input()

print("That is a nice name, " + name)
print("How old are you, " + name + " p.s. put a zero infront of a single digit")
age = input()

if age >= "18":
    print("if you're " + age + ", that means it's beer o'clock!")
diff = str(18 - (int(age)))
if age < "18":
    print("That means you have to wait " + diff + " years to have a drink on me!")

In Line 9 you're comparing two strings.
The comparison of str is made via lexicographical order.

Here are some hexadecimal values:
Whitespace == 0x20
0 - 9 == 0x30 - 0x39
A - Z == 0x41 - 0x5a
a - z == 0x61 - 0x7a

If you compare this:
"1" > "18"

The interpreter compares char by char.

(0x31,) > (0x31, 0x38)

But if you compare "4" > "18", you have this values:

(0x34,) > (0x31, 0x38)

So, the first one is bigger and this explains why "4" > "18" == True.

If you want to compare numbers, then convert the str into int.

print("hello world!")
print("What is your name?")
name = input()

print("That is a nice name, " + name)
print("How old are you, " + name + " p.s. put a zero infront of a single digit")
age = int(input())

if age >= 18:
    print("if you're " + str(age) + ", that means it's beer o'clock!")
diff = 18 - age
if age < 18:
    print("That means you have to wait " + str(diff) + " years to have a drink on me!")

The concatenation of str should not be done with + operator. If you work with int, float or other types, you've to convert them back to a str. Instead, use string formatting. With modern Python, we have f-strings. A f in front of the " introduces a format-string. The names in the curly braces are replaced with their values. For example, {age} is replaced with the age, which is an int.

print("hello world!")
print("What is your name?")
name = input()

print(f"That is a nice name {name}")
print(f"How old are you {name}")
age = int(input())

if age >= 18:
    print(f"if you're {age} that means it's beer o'clock!")
diff = 18 - age
if age < 18:
    print(f"That means you have to wait {diff} years to have a drink on me!")

The benefit is, that you don't have to convert the int explicit back to a str if you're using string formatting.