The sentences do have the same meaning.
In the first sentence – "In the centre of town" – it is probable that the speaker and the listener already know which town is being mentioned. It is a town known to both.
In the second sentence – "In the centre of the town" – the speaker is most likely referring to a town that the listener doesn't know or hasn't heard of. The speaker might, for example, be describing a town s/he visited on a trip. After more discussion, however, the speaker may assume that the listener is now familiar with the town and may omit the definite article.