"He's not just my client, he's my friend."

Most fitness professional organisations will have a Code of Ethics which includes something like, "the trainer should ensure they do not form a personal relationship which might compromise the professional relationship." What they mean is, "keep it in your pants," but it applies to other kinds of relationships as well. This is difficult because a trainer and client will spend a lot of time with each-other, you the trainer will see the client in vulnerable moments - both failure and success - and clients will generally trust and open up to you in surprising ways. 

Some things for a trainer to think about are below. This is useful for clients as well, of course. 

You can be friends with a client, but there are limits. Essentially you don't want to be a dickhead in front of a client, nor overly familiar. They should not see you drunk and vomiting, or grinding on chicks/guys at the club. If you have problems with your husband or mother, don't talk about them to your client. Especially don't badmouth your colleagues or boss to the client-friend. Any gifts you give to your client-friend should be related to their physical training, like weightlifting shoes, a new set of cricket pads or whatever. 

As a trainer, you'll tend to find that the friendship is rather one-sided and won't last past the training. If they're sick you'll call and see how they are, you'll remember their kid's birthday, that sort of thing. They won't do the same. As well, once the training relationship is over, the friendship will fade away. It's like when you stop working at some place, and your workmates say, "hey, we gotta catch up, let's do lunch sometime." You never will. Take away the common activity and the relationship is dead. They were just friendly, not your friend. 

Since they're your client in your workplace where you spend 20-60 hours a week, they're a big part of your life. But you are only 1/2 to 3 hours a week of their life. They may spend more time each week with Simpsons repeats than they do with you. Outside training, and after the training stops, you'll be well-thought of until you're forgotten shortly afterwards. This is disappointing but there it is, you won't get your fill of social life from the gym, same as any workplace, you need to have a life outside work. 

There are exceptions of course but these are the general rules.