血 can be used in all abstract senses, while 血液 is necessarily the substance that runs through your veins.
Hence, if you want to say that you are “connected by blood” as in family member, you say 血で繋がっている. If you try saying something like 血液で繋がっている it sounds like you had a blood transfusion from that person or something like that.
Also, 血液 usually has a nuance of still inside the body, as in, alive. I assume there should be some exceptions to that, but for example if you see a blood spill on the floor you are gonna shout 血, but definitely not 血液.
Lastly, 血液 sounds more fancy academic, so scientific terms related to blood will usually use it, such as 血液型 or 血液検査