These two terms, while related, are not the same. They both result in delayed germination, but for different reasons.
Hard seed is seed that are delayed mostly because of an extra hard seed coat. This can be a function of the species and also of the conditions as the seeds are forming and maturing. For some plant species, it is normal for a small or moderate percent of the seed to be hard seed. This is common in leguminous species. This seed is still viable, but germination will be slower. The number of hard seeds decreases after storage, which varies in time for different crops from several weeks to several years. Some other species are known for producing mostly seeds with very hard seed coats. Asparagus and Canna Lilly come to mind.
Germination of both of these types of hard seeds can be sped up by a few different practices. Physically piercing the seed coat or abrading the seed coat to allow easier transfer of water and oxygen are the most common methods. Chemical stratification to soften the seed coat can also work. Cold stratifying, as discussed below, can also often improve germination of these seeds.
Dormant seed is a related condition where the seed normally requires specific conditions or a sequence of conditions to enable germination. The most common of these is seeds requiring cold stratification. That is holding the seeds in moist, low temperature conditions for a period of time, then bringing up the temperature to a suitable figure for germination. One common practice is to store these seeds in a moist paper towel in a sealed container in a refrigerator for several weeks, then starting them in a light garden indoors. This can also be accomplished buy planting out doors in the fall and allowing them to come up naturally in the spring. This outdoor practice is common for some popular flower species.