Here is a snippet in python. Or you can try out the biopython module too. But be aware this guessing work can go very wrong if you have UIPAC nucleotide symbols other than ATCG. https://www.bioinformatics.org/sms/iupac.html

https://colab.research.google.com/drive/1XSQBDoLIyQUGwUJvXRtZHkcXxsVU6oRH?usp=sharing

with open('example.fasta', 'w') as f:
  f.write('>seq1DNA\nATCG\n>seq2DNA\nTCGT\nTCTC\n>seq1Protein\nSSTCG\n>seq2Protein\nHYRN\nKQES')
from collections import defaultdict
def fastaparser(fasta):
    '''
    Read fasta file and return a dict, each record with seq name as key
    '''
    records = defaultdict(list)  
    with open(fasta,  'r') as f:
        lines = f.read().split('\n')[:-1]
        for line in lines:
            if line.startswith('>'):
                key = line
                continue
            records[key].append(line) 
    f.close()
    return records
DNA_alphabet = {'A', 'T', 'C', 'G'}
for k, seqs in records.items():
  if len(set("".join(seqs)).union(DNA_alphabet)) > 4:
    with open('protein.fa', 'a') as f:
      f.write(f"{k}\n")
      f.write(f"{''.join(seqs)}\n")
  else:
    with open('DNA.fa', 'a') as f:
      f.write(f"{k}\n")
      f.write(f"{''.join(seqs)}\n")