diff --git a/pandas/core/arrays/base.py b/pandas/core/arrays/base.py
index eae401f9744f0..c2fc72ff753a8 100644
--- a/pandas/core/arrays/base.py
+++ b/pandas/core/arrays/base.py
@@ -32,7 +32,7 @@
 
 from pandas.core import ops
 from pandas.core.algorithms import factorize_array, unique
-from pandas.core.missing import backfill_1d, pad_1d
+from pandas.core.missing import get_fill_func
 from pandas.core.sorting import nargminmax, nargsort
 
 _extension_array_shared_docs: Dict[str, str] = dict()
@@ -616,7 +616,7 @@ def fillna(self, value=None, method=None, limit=None):
 
         if mask.any():
             if method is not None:
-                func = pad_1d if method == "pad" else backfill_1d
+                func = get_fill_func(method)
                 new_values = func(self.astype(object), limit=limit, mask=mask)
                 new_values = self._from_sequence(new_values, dtype=self.dtype)
             else:
diff --git a/pandas/core/missing.py b/pandas/core/missing.py
index c2926debcb6d6..f3229b2876e5d 100644
--- a/pandas/core/missing.py
+++ b/pandas/core/missing.py
@@ -562,20 +562,22 @@ def interpolate_2d(
         values = values.reshape(tuple((1,) + values.shape))
 
     method = clean_fill_method(method)
+    tvalues = transf(values)
     if method == "pad":
-        values = transf(pad_2d(transf(values), limit=limit))
+        result = _pad_2d(tvalues, limit=limit)
     else:
-        values = transf(backfill_2d(transf(values), limit=limit))
+        result = _backfill_2d(tvalues, limit=limit)
 
+    result = transf(result)
     # reshape back
     if ndim == 1:
-        values = values[0]
+        result = result[0]
 
     if orig_values.dtype.kind == "M":
         # convert float back to datetime64
-        values = values.astype(orig_values.dtype)
+        result = result.astype(orig_values.dtype)
 
-    return values
+    return result
 
 
 def _cast_values_for_fillna(values, dtype: DtypeObj, has_mask: bool):
@@ -597,10 +599,9 @@ def _cast_values_for_fillna(values, dtype: DtypeObj, has_mask: bool):
     return values
 
 
-def _fillna_prep(values, mask=None, dtype: Optional[DtypeObj] = None):
-    # boilerplate for pad_1d, backfill_1d, pad_2d, backfill_2d
-    if dtype is None:
-        dtype = values.dtype
+def _fillna_prep(values, mask=None):
+    # boilerplate for _pad_1d, _backfill_1d, _pad_2d, _backfill_2d
+    dtype = values.dtype
 
     has_mask = mask is not None
     if not has_mask:
@@ -613,20 +614,20 @@ def _fillna_prep(values, mask=None, dtype: Optional[DtypeObj] = None):
     return values, mask
 
 
-def pad_1d(values, limit=None, mask=None, dtype: Optional[DtypeObj] = None):
-    values, mask = _fillna_prep(values, mask, dtype)
+def _pad_1d(values, limit=None, mask=None):
+    values, mask = _fillna_prep(values, mask)
     algos.pad_inplace(values, mask, limit=limit)
     return values
 
 
-def backfill_1d(values, limit=None, mask=None, dtype: Optional[DtypeObj] = None):
-    values, mask = _fillna_prep(values, mask, dtype)
+def _backfill_1d(values, limit=None, mask=None):
+    values, mask = _fillna_prep(values, mask)
     algos.backfill_inplace(values, mask, limit=limit)
     return values
 
 
-def pad_2d(values, limit=None, mask=None, dtype: Optional[DtypeObj] = None):
-    values, mask = _fillna_prep(values, mask, dtype)
+def _pad_2d(values, limit=None, mask=None):
+    values, mask = _fillna_prep(values, mask)
 
     if np.all(values.shape):
         algos.pad_2d_inplace(values, mask, limit=limit)
@@ -636,8 +637,8 @@ def pad_2d(values, limit=None, mask=None, dtype: Optional[DtypeObj] = None):
     return values
 
 
-def backfill_2d(values, limit=None, mask=None, dtype: Optional[DtypeObj] = None):
-    values, mask = _fillna_prep(values, mask, dtype)
+def _backfill_2d(values, limit=None, mask=None):
+    values, mask = _fillna_prep(values, mask)
 
     if np.all(values.shape):
         algos.backfill_2d_inplace(values, mask, limit=limit)
@@ -647,7 +648,7 @@ def backfill_2d(values, limit=None, mask=None, dtype: Optional[DtypeObj] = None)
     return values
 
 
-_fill_methods = {"pad": pad_1d, "backfill": backfill_1d}
+_fill_methods = {"pad": _pad_1d, "backfill": _backfill_1d}
 
 
 def get_fill_func(method):
@@ -724,7 +725,7 @@ def inner(invalid, limit):
     return f_idx & b_idx
 
 
-def _rolling_window(a, window):
+def _rolling_window(a: np.ndarray, window: int):
     """
     [True, True, False, True, False], 2 ->