They’re different things.

A family tree is a representation of your ancestry by tracing backwards (usually, some people use the term for anything related to family ties). It’s backwards in time, almost always.

Your bloodline is forwards in time from ancestor. The idea is that there is a clear line of descent from one person, or a small group (depending on how it’s being applied in context).

Think of it in terms of race horses.

Secretariat had a family tree of horses before he came along. He had a dam and sire. They had dams and sires, and so forth. The tree, when laid out, may include siblings of secretariat, but wouldn’t include “nieces and nephews” under normal circumstances because that’s not really the point of the family tree as a term/idea. That steps into general genealogy.

However, from secretariat, you can trace records of horses descended from him, and that’s literally his bloodline. That’s his genetic line where his semen was used to make other horses.

Unlike horses, you couldn’t guarantee paternity for humans until genetic testing came along. At best, you could exclude someone via blood typing, or some inherited features (like a cleft chin).

The term bloodline itself started before knowledge of genetics was a thing to any serious degree. Mendel didn’t do his thing until the 1800s, and bloodline is a compound word that goes back 200 more years. But it is related as an idea. Related being the key word to that.

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To reframe it, I have a family tree that includes a wide range of ancestors going back to Europe before we can’t find anything on either my matrilineal, or patrilineal side. Both my father’s surname and my mother’s maiden name have been traced back as far as the 1700s. However, my “bloodline” descends from the oldest known ancestor, a man that had a different name because it was in German instead of being anglicized. It also descends from multiple other people, but you could trace each of those and determine who else shares that bloodline.

Me and my sister are the only living people that have the exact same family tree, but we share any given bloodline with thousands (at least) of known individuals.