'抓' is just an action, but the result is unknown. '抓' means 'be catching at sth. or sb.'. '抓住' not only describe the action, but also give out the result. '抓住' means 'sth. or sb. has been caught hold of'.

抓，it is a verb ，is happening。 抓住，can be understand ... have done eg: 警察去抓那个坏人了。（抓） 警察已经抓住那个坏人了。（抓住）

抓 is an action. 抓住 is an outcome. 她努力想抓树上的小鸟，但是没有抓住。

抓is a verb,抓住is the result of 抓

抓 is an action while 抓住 describes the status or result.