diff --git a/sklearn/metrics/pairwise.py b/sklearn/metrics/pairwise.py
index 1a70d2e4fbcea..fa90dedb06da7 100644
--- a/sklearn/metrics/pairwise.py
+++ b/sklearn/metrics/pairwise.py
@@ -284,7 +284,7 @@ def euclidean_distances(
     X, Y=None, *, Y_norm_squared=None, squared=False, X_norm_squared=None
 ):
     """
-    Compute the distance matrix between each pair from a vector array X and Y.
+    Compute the distance matrix between each pair from a feature array X and Y.
 
     For efficiency reasons, the euclidean distance between a pair of row
     vector x and y is computed as::
@@ -2276,12 +2276,21 @@ def pairwise_distances(
     ensure_all_finite=None,
     **kwds,
 ):
-    """Compute the distance matrix from a vector array X and optional Y.
+    """Compute the distance matrix from a feature array X and optional Y.
 
-    This method takes either a vector array or a distance matrix, and returns
+    This function takes one or two feature arrays or a distance matrix, and returns
     a distance matrix.
-    If the input is a vector array, the distances are computed.
-    If the input is a distances matrix, it is returned instead.
+
+    - If `X` is a feature array, of shape (n_samples_X, n_features), and:
+
+      - `Y` is `None` and `metric` is not 'precomputed', the pairwise distances
+        between `X` and itself are returned.
+      - `Y` is a feature array of shape (n_samples_Y, n_features), the pairwise
+        distances between `X` and `Y` is returned.
+
+    - If `X` is a distance matrix, of shape (n_samples_X, n_samples_X), `metric`
+      should be 'precomputed'. `Y` is thus ignored and `X` is returned as is.
+
     If the input is a collection of non-numeric data (e.g. a list of strings or a
     boolean array), a custom metric must be passed.
 
@@ -2289,15 +2298,11 @@ def pairwise_distances(
     preserving compatibility with many other algorithms that take a vector
     array.
 
-    If Y is given (default is None), then the returned matrix is the pairwise
-    distance between the arrays from both X and Y.
-
     Valid values for metric are:
 
     - From scikit-learn: ['cityblock', 'cosine', 'euclidean', 'l1', 'l2',
-      'manhattan']. These metrics support sparse matrix
-      inputs.
-      ['nan_euclidean'] but it does not yet support sparse matrices.
+      'manhattan', 'nan_euclidean']. All metrics support sparse matrix
+      inputs except 'nan_euclidean'.
 
     - From scipy.spatial.distance: ['braycurtis', 'canberra', 'chebyshev',
       'correlation', 'dice', 'hamming', 'jaccard', 'kulsinski', 'mahalanobis',
@@ -2570,15 +2575,15 @@ def pairwise_kernels(
 ):
     """Compute the kernel between arrays X and optional array Y.
 
-    This method takes one or two vector arrays or a kernel matrix, and returns
+    This function takes one or two feature arrays or a kernel matrix, and returns
     a kernel matrix.
 
-    - If `X` is a vector array, of shape (n_samples_X, n_features), and:
+    - If `X` is a feature array, of shape (n_samples_X, n_features), and:
 
       - `Y` is `None` and `metric` is not 'precomputed', the pairwise kernels
-        between `X` and itself are computed.
-      - `Y` is a vector array of shape (n_samples_Y, n_features), the pairwise
-        kernels between arrays `X` and `Y` is returned.
+        between `X` and itself are returned.
+      - `Y` is a feature array of shape (n_samples_Y, n_features), the pairwise
+        kernels between `X` and `Y` is returned.
 
     - If `X` is a kernel matrix, of shape (n_samples_X, n_samples_X), `metric`
       should be 'precomputed'. `Y` is thus ignored and `X` is returned as is.