As people before me have already stated; Al's gate is from The Marrow of Alchemy. If I remember correctly, the symbol represents purification, and it is believed that the only way to obtain total purification is to get rid oneself of their physical body (something Al is pretty familiar with).
Roy's gate is a lot more complicated than that. Yes, parts of his gate are shown on Riza's tattoo; however the parts on his gate do not represent flame alchemy as many people believe, but instead the sun and the serpents represent something called the marriage of the Red King and White Queen. Basically Roy and Riza's relationship is an analogy for the Red King and White Queen.
It's a little complicated, but here's a YouTube video where I go a bit more into depth about Roy's gate.