Blood plasma is the intravascular fluid part of extracellular fluid (all body fluid outside of cells). It is mostly water (up to 95% by volume), and contains dissolved proteins (6-8%) (i.e.-serum albumins, globulins, and fibrinogen), glucose, clotting factors, electrolytes (Na+,Ca2+,Mg2+,HCO−3,Cl−, etc.), hormones, and carbon dioxide (plasma being the main medium for excretory product transportation).
Plasma in Sun is ionized gas formed by heating a gas or subjecting it to a strong electromagnetic field. This plasma is one of the 4 fundamental states of matter.
So certainly, these two are not same. As far as having the same name is concerned maybe both of them are named so because they contain ions and are mixtures of many components. The word plasma means shape.