These 2 exercises do not train the same muscles.
Romanians work the glutes, Stiff legs work the hamstrings.
Depending on which muscle you want to train, you do the respective exercise.
Often times they can look similar depending on someone’s proportions, but the intent of each is very different.
You can include both in a program, although I would probably not do both of them in the same work out.
Both of these can be done with barbell, dumbbells, kettle bells, cables, trap bar, etc.
I personally prefer dumbbells for Romanians and the barbell for stiff legs, But find what works for you.