To add to the above answer: The odds of obtaining either of those combinations are 1 in 8. If you take each flip as a individual "experiment" with two possible outcomes, the odds of each are 1 in 2. To get the probability of any outcome of two tosses (HH, HT, TH, TT) you'd multiply the odds of each together (1/2 * 1/2). You can extend this as far as you want... in other words for each flip you multiply another 1/2.
Now looking at your two samples... THT, THH... there is a 1 in 4 chance that ONE of the two will appear, since the only difference is the last toss. But, as was already stated... the probability is exactly the same that either will occur first.
You can extend this to dice, as well... say you want to know the probability of getting 421 on three tosses... you'd multiply (1/6)(1/6)(1/6), to get a probability of 1 in 216.
Now, with that being said... let's look at your combinations a bit further. If we are starting from scratch and counting how many tosses it takes to get a certain pattern, things change...
If we are looking for THT, and we get the first two right (TH) and miss the last... we have to start from scratch again... not to bore you with systems of equations, but on average you will take 10 tosses to get this pattern from scratch.
If we are looking for THH, and we get the first two right (TH) and miss the last (getting a THT)... we STILL get a little better odds of getting the pattern again, because we've already started with a "T." Once again, not to bore you with systems of equations, you will average 8 tosses to get this pattern. The difference lies in the fact that you get a "head start" on matching it again if you miss the pattern.
COMMENT/EDIT: For the above discussion, I assume we start each experiment fresh... and count until we get the combination we desire. In that case, the THH combination will occur sooner more times than the other combination of THT. In other words, we are looking for one only to occur... not either/or. The bonus question asks for each pattern exclusively... not looking for both.
I know I overanswered the question... but many people have problems with this principle. If you want more, very technical details on this phenomenon, look up a "Markov chain" and get ready for some serious number crunching.