Mashed (or riced) potatoes are done by hand where the mashing takes place with a masher and then butter and/or milk are added at the end and stirred in.  For whipped potatoes, the potatoes are whipped or beaten with a hand mixer with the butter and cream added and whipped together. Mashing tends to not activate too much starch and holds them intact for a lumpier recipe. Whipping adds air and can activate starch for a soft or fluffy texture.