"打" is a general word. The particular connotations depend on the different contexts or its modifiers. Just like you know, the smallest component is “character”, rather than "word". Hence one character in Chinese may be more ambiguous than a word in English, especially in Modern Chinese.
For example, "暴打" implies “beat”,or strongly hit, etc. "轻轻地打了一下" implies “pat”, "一巴掌打在脸上" means “smack on one’s face”, "一拳打在脸上" means “punch in one‘s face”. "打了一顿" means 打了 for several times; “打了一下” means for only one time.
In terms of your question, normally, hit=击, punch=捶, smack=扇, beat=打. But when we say "父母打孩子", "打" here is ambiguous. It could be "punch", "smack","beat", even can use a tool, etc. Despite this, the most common one is "smack on a kid's buttocks".