What is the difference between a brad nailer and a finish nailer. and does
one hold wood peices better than the other.

The two terms are often used together. Generally, a brad nailer is 18ga, and
the nails range in length from about 5/8" to 2". A finish nailer is usually
15ga or 16 ga and the nails vary in length from about 1" to 2.5". When you
go to buy nails, they're all called finish nails, whether they're 15, 16, or
18ga. The difference in terminology applies to the guns more than the nails.

Obviously the 15ga, because of the larger nail, has better holding power.
The 15ga nail, being more rigid, is more likely to go straight and not
follow the grain, as happens often with 18ga nails.

Some like to use the brad nailers for trim work due to the smaller hole it
leaves behind. Others like to use the 15ga nailers for their better holding
power and slightly longer nails (useful for crown molding, etc.).