The coin one is probability - there is still a possibility you get tails four times running. If you are looking for two heads, it is only at the start of the run of tosses that the chance of two heads turning up is one in four. At each toss there is a one in two chance of heads, so each time you toss, you have a chance of being lucky or unlucky.
The sock one is also probability, but you are not looking specifically for two grey ones, so if you get a brown one first time, you don't mind. The second time, it could also be brown - (good, you now have a pair!) - but it could be grey - (OK, you now have one of each - but on the third go you have a match to one or other of them), so you have a pair at three shots at the most.