Summary
Being a GPGPU product, the Tesla series lacks the display output (Except the latest Tesla C-class series GPUs, where it includes one Dual-Link DVI port). The brand name is also the name of the GPU architecture of the same name.
Generations
Tesla based
The first Tesla GPU family based on Tesla architecture. The S-class models are the 1U rack form-factor, and the D-class model is a Deskside GPU. Other models are in the standard graphics card form factor.
C870, D870 and S870 supports CUDA compute capability 1.0, while C1060 and S1070 supports CUDA compute capability 1.3.
Fermi based
The second-generation Tesla GPU family is based on the Fermi architecture. Only the S-model (S2050) is in the 1U rack form-factor.
All models supports CUDA compute capability 2.0.
Kepler based
The third-generation Tesla GPU family is based on the Kepler architecture. Only the K10 is a dual-GPU GPGPU.
Only the K10 model supports up to CUDA compute capability 3.0, while the other (GK110-based) are supports up to CUDA compute capability 3.5 and OpenCL 1.1.
The interest note is that GK110 make its debut on Tesla GPU family, and was later introduced in the GeForce GPU family (GTX Titan, GTX Titan Black, GTX Titan Z, GTX 780, GTX 780 Ti) and in the Quadro GPU family (K6000).
See Also
GeForce - Tesla's gaming-orientated counterpart
Quadro - Tesla's workstation-orientated counterpart
Nvidia - The company which produces the Tesla GPU family