Final answer:
Elizabeth Cady Stanton used a different phrase to distinguish between different societal groups, particularly immigrants and middle-class white women. She believed that including women in the language of the amendments was important to counter the influence of certain groups.
Step-by-step explanation:
Elizabeth Cady Stanton used a different phrase instead of 'one people' because she wanted to highlight the distinction between different groups within society. She frequently contrasted the 'lower orders' of immigrants with middle-class white women who were denied suffrage. Stanton argued that the inclusion of women in the language of the amendments was necessary to counter the influence of uneducated freedmen in the South and poor European immigrants arriving in the East.