Yep, it's completely different! "Albumin" is just a word for "water-soluble protein" - these are usually shaped sort of spherically, which is why they disperse in water and distribute evenly through it.
Egg white has a lot of ovalbumin and some other water-soluble proteins in it. Blood has "human serum albumin", which is an entirely different water-soluble protein. The molecular structures of the two water-soluble proteins are not very similar - ovalbumin has 385 amino acids and human serum albumin has 585, so different shapes and masses, both roughly spherical. (They might say "globular".)
The reason albumins generally would help to transport things in solution would just be that they'd tend to form colloid solutions - drop some into a glass of water, and it will disperse throughout the water and thicken it up a bit, like egg white or blood, and push on the other stuff dissolved in the solution.
