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Menstrual blood IS both tissue and the blood that provided the endometrium lining with nutrition during its building up process. It contains an enzyme that keeps it from clotting. Think of it as a disintegrating organ.
Regardless of its structure, menstrual blood has a lot of magical connotation for most of us. It comes from woman, the sacred womb and is tied (symbolically) to the moon. "O cup, o sacred chalice of the Goddess"
The acquisition of such blood is done without violence and the use is typically a way of binding self to spell (the "price" of a spell was previously mentioned in this thread). Many will use this blood in a coming of age ritual. It's also a really good fertilizer! Try some in a ritual for plant fertility and give some mixed with water to the plants in your home.
Standard blood is strong in that it is your life, really. It carries all that keeps you functioning through your veins and when you give some of it to a spell, it is a sacrifice of high honour. Voodoo/Voudou practitioners will mix blood with rum as a great sacrifice to their gods when asking for the big stuff.
Since the coming of AIDS/HIV and the realization that we have blood-borne diseases, the use of blood has been relegated to the truly hidden things witches do. We can use our own and that of those we trust.
Never ever STEAL someones blood.
If you practice a faith that uses animal sacrifice I URGE you to learn from leaders in your community so that it is done well and with respect to the animal (and local laws!).
I do not practice animal sacrifice, myself. If a spell needs blood, it will be my blood.
Speaking of which, donate blood, guys. It's a bit of your magic to save someone else. How much more could you honour your fellow humans than by giving of your life for theirs?

On this topic, I'll be attending an interesting ritual for Litha. I'm told it's a possession ritual and there will be blood magic involved. Each participant will only use thier own blood of course. I've never been to anything like this though I have attended several of thier rituals before. I'm very curious and a bit nervous but I trust the abilities and knowledege of the people performing it.