They are about as different as you can imagine other than the fact they use a similar fuel. Diesel and jet fuel are often interchangeable, that is true, in fact you can fill a Diamond Piston Diesel with jet fuel, that engine is based on a Mercedes 2 liter automobile engine.

A turbine is any device that is spun due to something pressing against a medium. A fluid turbine turns because a fluid passes over the vanes and moves the, a gas turbine does the same thing but with a gas. There isn't an articulating motion, the more pressure you send through the vanes the faster it spins and the more power you can create. The turbine is a specific part of the engine, the whole thing is called a turbine but if you plow a fan through a tube which has a rod along the long axis and at the end are some veins, that is also a turbine. Those big spinny things they build in fields are also turbines. In a gas turbine like you are talking about, you use compressor stages to compress the air before it hits the actual turbine. Everything spins along a shaft(s).

A diesel engine works by compressing an air/fuel mixture and combusting it such that it pressures the piston back down allowing another piston on the same crankshaft to rise to compress or exhaust. Assuming the combustions create more power than needed to keep the crank spinning you can attach a shaft to the crank and create spinning power.

Articulating devices are far harder on the metals than ones that simply spin, there are some diesels and gasoline engines that are capable of rotating at very high speeds but physics limits you. A turbine, on the other hand, only spins, and since you aren't sending something of mass out and back again (like a piston) your physical limits are a lot higher. Your reciprocating mass on a piston engine is far higher, the faster you go the more apparent mass on your components. A turbine will hit a limit as well, but they are at much higher RPMs.