In your second function you apply any to a single element and not to the whole list. Thus, you get a single bool element if character i is alphanumeric.

In the second case you cannot really use any as you work with single elements. Instead you could write:

for i in s:
    if i.isalnum():
        print(True)
        break

Which will be more similar to your first case.

You seem to think isalnum returns True if a string contains both letters and numbers. What it actually does is return True if the string is only letters or numbers. Your last example contains a space, which is not a letter or number.

You can build up the functionality you want:

words = ["cyberpunk" ,"x10", "hacker" , "x15" , "animegirl" , "x20", "this sucks"]

def hasdigit(word):
    return any(c for c in word if c.isdigit())

def hasalpha(word):
    return any(c for c in word if c.isalpha())

def hasalnum(word):
    return hasdigit(word) and hasalpha(word)

for word in words:
        print word,'/',hasalnum(word)

Output:

cyberpunk / False
x10 / True
hacker / False
x15 / True
animegirl / False
x20 / True
this sucks / False