There isn't a significant difference in meaning.
Constructions like this, using what is known as 'delexicalised' verbs, are very common in everyday English. We often put the important information in the noun - 'a sip' - and make a verb phrase with it using a very neutral and all-purpose verb such as 'take' or 'have'. 'Have a look at this' or 'Take a look at this' as opposed to 'Look at this' is a common example.
As a general rule, the 'take' version tends to be more common in American English. For example, an American English speaker would say 'take a shower' or 'take a walk', while a British English speaker would say 'have a shower' and 'go for a walk'.