「使う」は、日本人なら小さな子どもでもわかる言葉です。よく使う言葉です。 「使用する」は、少しformal な言葉です。

As Ryan mentioned, you can use tsukau for almost everything, but Shiyou is limited and sounds more formal or official. For example, a mom tells her kid "ハサミを使いなさい” , sounds perfect, but "ハサミを使用しなさい" sounds weird. Also, you have to choose tsukau or shiyou depend on the subject. For example, "時間を使った" is possible, but "時間を使用した" is not. I hope this helps!

i dont know btw. base on the dictionary, tsukau seems to have that abstractness to it. use language, use time, use person. the shiyou, seems like using a thing. can probably interchange between the two, imo.