While all three of these are similar or even identical there are some nuances between them. Catherterophilia is the medical side of cather play. There is a large group of people who are into medical play for sexual enjoyment. This is not about urine but the process itself that they enjoy. This type of play is done as if it were in a medical setting and is all about the steps involved and the control in this case of the bladder. Urethra is more the sexual side of this play it is still done generally with a cather but it is more about working someone up and then using that to give them an intense orgasm. The only difference between Catherterophilia and Urethra is the setting the acts are still about the same.
Sounding is using solid rods in the place of cathers. It is about the stretching sensation of using larger rods in place of others. It is also about the feeling of having the urethra stimulated from the inside. A lot of people think that this type of play is new but it has been documented from as long ago as 4000 years. Like most fetishes they are not new to our time frame. These fetishes do require skills to be learned and a number of safety precautions as to not harm someone. These areas of the body are fragile to some degree and one can cause a lot of harm very quickly that will require medical intervention. This type of play is not for people who are lazy on the clean side. Infections can be common even under the best situations. It is important to make sure that everything is kept sterile at all times. Sounding has become more popular in the last couple of years and with it a lot of men are trying it on themselves. With a little practice and going very slow at first it can bring on intense orgasms. It can increase the fluid produced during orgasms to a much higher volume. I have had men explain that a handjob combined with sounding is a sensation they can not even describe in words. If you were wondering what would have been used in ancient times for this type of play the most common were bone, antler, and ivory. Now we have much better play things such as stainless steel and glass (though breakage might be frighting to some).