IN PRIME'S YOU ALWAYS KEEP A CONNECTED COMPONENT , STARTING WITH A SINGLE VERTEX. YOU LOOK AT THE ALL EDGE FROM THE CONNECTED COMPONENT TO THE OTHER VERTEX AND FIND SMALLEST AMONG THEM. YOU THEN ADD THE NEIGHBORING VERTEX TO THE COMPONENT, INCREASING ITS SIZE BY ONE TO THE CURRENT COMPONENT ,IN N-1 STEPS EVERY VERTEX WOULD BE MERGED WITH THE CURRENT ONE IF WE HAVE A CONNECTED GRAPH.
IN KRUSKAL'S YOU DO NOT NEED TO ONE CONNECTED COMPONENT BUT A FOREST AT EACH EDGES YOU LOOK AT THE GLOBALLY SMALLEST EDGE THAT DOESN'T CREATE A CYCLE IN CURRENT FOREST SUCH AN EDGE AS TO NECESSARILY MERGE TO THE TWO TREES IN THE CURRENT FOREST INTO ONE IF THE GRAPH WAS CONNECTED