I would use pandas.concat with slicing to do this:
import pandas as pd
df = pd.DataFrame({
    'ORD_DATE':['1/1/2020'],
    'Weekday':[2],
    'ALL Sales':[48386.27],
    'ALL Pred':[20815269.83],
    'Other Sales':[15386.27],
    'Other Pred':[5643158.509],
})
df2 = pd.concat([
    df[['ORD_DATE','Weekday','ALL Sales','ALL Pred']].rename(columns={
        'ALL Sales':'Sales',
        'ALL Pred':'Pred',
    }),
    df[['ORD_DATE','Weekday','Other Sales','Other Pred']].rename(columns={
        'Other Sales':'Sales',
        'Other Pred':'Pred',
    }),
])
print(df2)
Output:
   ORD_DATE  Weekday     Sales          Pred
0  1/1/2020        2  48386.27  2.081527e+07
0  1/1/2020        2  15386.27  5.643159e+06
Example in python tutor
Edit With the Filter Column added:
import pandas as pd
df = pd.DataFrame({
    'ORD_DATE':['1/1/2020'],
    'Weekday':[2],
    'ALL Sales':[48386.27],
    'ALL Pred':[20815269.83],
    'Other Sales':[15386.27],
    'Other Pred':[5643158.509],
})
df_all = df[['ORD_DATE','Weekday','ALL Sales','ALL Pred']].rename(columns={
        'ALL Sales':'Sales',
        'ALL Pred':'Pred',
})
df_all['Filter'] = 'All'
df_other = df[['ORD_DATE','Weekday','Other Sales','Other Pred']].rename(columns={
        'Other Sales':'Sales',
        'Other Pred':'Pred',
})
df_other['Filter'] = 'Other'
df2 = pd.concat([df_all,df_other,])
print(df2)
Output:
   ORD_DATE  Weekday     Sales          Pred Filter
0  1/1/2020        2  48386.27  2.081527e+07    All
0  1/1/2020        2  15386.27  5.643159e+06  Other
python tutor link