The font size of .form-control in .input-group-sm is different from a single .form-control-sm when customize $input-font-size-sm or $input-btn-font-size-sm. The same is true for lg and .btn.

$input-font-size-sm: .5rem;
$input-font-size-lg: 2rem;

Demo: https://codepen.io/anon/pen/PyMyKo

One cause is related to the following lines:

• bootstrap/scss/_forms.scss

  Line 145 in 4b15ec9

  font-size: $input-font-size-sm;

• bootstrap/scss/_input-group.scss

  Line 149 in 4b15ec9

  font-size: $font-size-sm;