Why do these two pieces of code have different complexities?

Question

Both of these pieces of code do the same thing, which is they check if the words in the list magazine_words are sufficient to make up the message dictated by the words in the list note_words . However the first piece of code takes a lot more time to execute, which doesn't let it run for large inputs. Why is that? Since both solutions use single for-loops, shouldn't they have the same complexity, i.e. take about the same time to run?

First solution:

lengths = input().split ()
m = int(lengths[0])
n = int(lengths [1])
magazine_words = input ().split()
note_words = input ().split()
def checkMagazine(m,n,magazine_words,note_words):
  flag = "Yes"
  for ind in range (n):
    if not (note_words[ind] in magazine_words):
      flag = "No"
      break
    else:
      magazine_words.remove(note_words[ind])
  return flag
print (checkMagazine(m,n,magazine_words,note_words))

Second solution:

def ransom_note(magazine, ransom):
    rc = {} # dict of word: count of that word in the note
    for word in ransom:
        if word not in rc:
            rc[word] = 0
        rc[word] += 1

    for word in magazine:
        if word in rc:
            rc[word] -= 1
            if rc[word] == 0:
                del rc[word]
                if not rc:
                    return True
    return False



m, n = map(int, input().strip().split(' '))
magazine = input().strip().split(' ')
ransom = input().strip().split(' ')
answer = ransom_note(magazine, ransom)
if(answer):
    print("Yes")
else:
    print("No")```

Answer 1

magazine_words.remove(note_words[ind]) is secretly another loop - this has to loop through all of magazine_words until it finds note_words[ind], each time you call it.