AdWords is a Google service to advertise your website. Since it doesn't matter if you use it or not and you still have the limit. Go ahead and use t if you please.
AdSense is a Google service to put advertisement in your webpage. Until what I remember there is no problem on using it on your website.(as long as you follow the ToS here and in AdSense)
adwords makes it easy for big buisnesses post their ad to get more visitors
so if your not a popular website then $25 might last longer than expected mabye months