달리다 only means running or sprinting. 뛰다 can mean 달리다, but it can also mean to jump or leap. You can see it in the names of olympic sports. 100미터 달리기 (100 meter sprint), 넓이뛰기 (long jump), 높이뛰기 (high jump), etc. What you suggested is also partially true. Since 달리다 tends to be more serious running, running to catch a cab is more often described with 뛰어가다 than 달려가다, although both are possible.