#05AB1E, 9 8 bytes

Code:

lvyð-{}Q

Explanation:

l         # Lowercase the strings
 vy   }   # Map over the list, for each...
   ð-     #   remove spaces
     {    #   and sort
       Q  # Check equality

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05AB1E, 9 8 bytes

Code:

lvyð-{}Q

Explanation:

l         # Lowercase the strings
 vy   }   # Map over the list, for each...
   ð-     #   remove spaces
     {    #   and sort
       Q  # Check equality

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#05AB1E, 9 bytes

Code:

2FIlð-{}Q

Explanation:

2F     }   # Do the following twice
  Il       # Read a line of input and convert to lowercase
    ð-     # Remove spaces
      {    # Sort the string
        Q  # Compare the two of them

This looks like the exact same submission of Luis Mendo Don Muesli

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#05AB1E, 9 8 bytes

Code:

lvyð-{}Q

Explanation:

l         # Lowercase the strings
 vy   }   # Map over the list, for each...
   ð-     #   remove spaces
     {    #   and sort
       Q  # Check equality

Try it online!