All "Classical Studies" assumes is that you have no previous experience of Classical languages (in terms of qualifications, that is). Its essentially the same degree. If you want to start languages from begginers level then go for classical studies. If you want to start from Intermediate or Higher level go for Classics.
Any degree in classics (be it studies or not) is very broad church: Languages, literature, politics, history, archaeology, art history, theology, philosophy etc etc etc. You are by no means disadvantaged by having "Studies" at the end of your degree title.