Car seat bases

Are they only compatible with their own brands? My sister in law just had a baby and I'm due in a couple months so my fiancé's mom will have 2 grand babies using the car seats. We plan on just getting her the bases for the car seats as opposed to her buying her own. My SIL has a Safety 1st car seat and I plan on getting a baby trend travel system. Would it just be easier for me to find a decent priced car seat for her to use or can they both use the same base?