What many people mean when they talk about a pursuit bike is a specialized bike geared for aerodynamics over steering or comfort.
The older ones typically would have a 650c wheel in front with a 700c in the rear. This leads to a "funny" looking bike..thus they are also called "funny bikes"
Well apparently al the aerodinamic TT frames are called persuit here in the US.. well actually a track persuit geometry bike (old school) uses a center of gravity lower AKA the bb is lower (KM TT frames are like that too), the angles are more like a road bike and a little bit longer.. basically lower, lighter and longer than a regular track bike used in a sprint or per points race.
The tubes were usually extremelly light, I remember one my mechanic did to me only for KM TT race. U were able to bend the tubes bare handed and it squezze as a twizlerr the 1st 100 meters (make sense right?) but after that was god darn stable (low center of gravity), with the time this configurations got transformed into aerodinamic bikes (80's- 90's) (funny bikes as zappcatt says), Nowadays I think the people is using those BH carbon frames with a triatlhon superman handlebars... so I have no clue if a persuit bike nowadays have an special geometry as in the past.
The next factor is that many factories are doing more like generan purpose frames than in the past too... well i hope the info could help u a little bit more