What's the difference in fluorescent lamps?
It kind of depends on where you are (UK?).  Your information doesn't match exactly with my experience with fluorescent-lamp sizes.  As I understand it, the number after the T in the designation is the diameter in 1/8ths of an inch (in the US anyway, I think elsewhere it is in mm).  Typical old style sizes in the US are T8 and T12 which would be 25mm and 38mm respectively.  The T5 series lamps would probably be the 16mm version you are referring to.

T5 lamps are electrically different from T8, although they are designed to be roughly the same Watts per unit length.  T5 lamps can only be run from an electronic ballast.  T5 lamps also produce more lumens per watt than T8, and run a little hotter.

T5 lamps are not compatible (physically or electrically) with T8 or T12 lamps, to make it work requires a conversion effort