Yes, it is a different study. The outcomes will never be exactly the same; the power of the high volume study will certainly be higher. If the outcomes go in the same direction as the smaller study it can be an validation study.
In my opinion, if the data are collected from different subjects, then the study can be considered as different. The interpretation of the outcome of the studies should be also different.
Yes, this is one of the hallmarks of high quality research. We must replicate studies in the same population (preferably by someone else) and in other populations or datasets (by you and others). One significant issue being debated in science is the insufficient replicaiton of studies; many scientists and journals don't want to conduct replications because they don't have the same "punchy" impact. However, this is an essential part of the research process. Another serious concern is the difficulty in publishing "Fail to reject the null hypothesis" results. If only positive results are published, ultimately research will be skewed. We must publish the success and the failures, in addition to your question of replication of the same methodology in different data.