All Rights or exclusive writes: This term means that the writer sells the publication all the rights to his or her piece. All Rights usually pays more but the writer loses possession of his or her work. Personally, I never sell All Rights to any piece I have written.
Assignments: This is when the publication gives a writer an assignment telling the writer what to write about. The publication then owns the rights to whatever work the writer has agreed to do on assignment. I do take assignments occasionally.
Regarding devotional writing, I freelance pieces under 1st rights, re-print rights, and also take assignments. When I freelance a piece, I write the devotion on any topic or verse I desire, send it to the publication hoping they will buy it. These are sold one at a time. If I take an assignment, the publication tells me what scripture passages to write about and usually assign five days at a time. Even though they will own the rights to my finished work, I will be guaranteed five days of devotions which, of course, will pay more.
In order to keep this blog post from being too long, I will write one more post about devotional writing. In it I will list some places where freelance devotions can be sent, as well as a few places that give assignments. I suggest building some freelance credits before you query asking for an assignment. The publications that make assignments will want to see samples of your work and know what other devotions you have written.