The cone of a driver can be made from a variety of materials:polypropylene, kevlar, paper, paper impregnated with carbon fiber or plastics or metallized, etc. There's no one answer as to which is best but each has its strengths and weaknesses. Keeping everything the same in a speaker driver and changing the material the cone is made from will result in changes in it's mechanical performance and behavior.
The speaker itself (cone, voice-coil, etc.) is attached to a chassis. It's a support mechanism, kind of like a basket. This basket can be made either using a casting process or say by stamping out the metal piece. Die casting is looked upon as a more robust process and everthing else benig equal, is stronger and more rigid. Look at as the difference between forging a knife blade or stamping one out of metal.
MPC metallescent cones sounds like some sort of take off on the material that the cone is constructed of. Guessing at the letters, it sounds like a cone that is made from a carbon filled polymer and further has a metal applied to it. Probably done to achieve certain design requirements as well as product differentiation.
GRIP chassis sounds like some sort of take of on what I said above. I guess it's not die cast though.
Manufacturers say a lot stuff that while somewhat important, is designed to convey to the consumer some uniqueness and mark of quality and sophistication as to what they're selling. It's kind of like me telling you that this drink I'm selling you is made from a unique combination of hydrogen that fuels the stars and oxygen which is needed to support life, joined together in a unique way and obtained by a proprietary process. Hey its only water but it sounds special doesn't it?