George and Lynne are on loungers with an unnamed friend. Lynne tells her that George and her are very much alike. The friend says she doesn't see that at all. George is glad to say that neither does he.
It looks like this is somewhere different from the local swimming baths. The baths have loungers but people don't usually talk on them. Also, Lynne has on an altogether different class of swimming costume. All this evidence suggests that George and Lynne are on a cruise.
On their cruise, George and Lynne have befriended a woman. She knows Lynne's name but doesn't know much about them. Lynne wants to tell her more and does so by comparing herself to George. This woman must have already spent a long time talking to George as she is able to make a judgement on Lynne's statement. She disagrees with it.
It is likely that Lynne was talking about her similarity to George in terms of habits and interests and she thinks that George is talking about physical similarities when he disagrees. He is in fact talking about habits and interests too. It has occurred to him that he and Lynne have nothing in common. He learnt this when talking to the woman the previous evening, someone with whom he has a lot in common with. This has forced him to question his reasons for being with Lynne. In the end he opts to stay with Lynne as he thinks that a good marriage is not worth wasting for a one night affair on a cruise.