MentalRay is mental images very stable, fast and physicaly oriented hybrid raytrace/scanline eingene! But you only get one licence worth of it you need to buy extra licendces for your renderfarm. Very eficcient, scalable and so on... but pretty high end if you want to do anything esoteric.
Maya SW is a older but still workagle renderer thats mainly meant for scanline render, its a bit quirky. Gets 99% of the job done if you have any technical aptitude and are ready to love oiling its parts. HAs certain advantages tough like ULTRA ACCURATE 3D motion blur, that costs more in rendertime than a small nation has capacity.
HW is basicaly a hookup of maya network nodes to the newest generation of programmable gpus (graphics card processor), as such ist fast but partialy limitted in many aspects, mostly if not completerly limitted to scanline rendering only, altough certainly if you want to code yoruself it is possible to get raytracing availeable. Basicaly the same as the highquality views of viewports with multisampling and moblur oversampling.
Then theres the old HW renderer (hw buffer), wich is basicaly may astandard viewport stuff. with multisampling.
And finaly theres the vector renderer that does a analytical render of the trangles convertting them to vector data. Usefull for some cool stuff but in general teh msot limitted renderer. However with some comp, it realy makes worth the effort especialy for cartoon edges if mr isnt your poison of choise (in fact it can be better then mr in soem cases for line stuff, altough a bit akward to work with for line weights).