I think in the first and 2nd rounds you are usually drafting for people who can come in an play in the rotation immediately. The 4th round on you are drafting players that you hope to develop for the future and players that can excel on special teams. You are probably looking a year ahead and filling needs for rotation players and starters where you have contracts that will come up or need depth. In the 3rd round you are probably hoping for someone who can grow into a rotation player during the season and can maybe even start later in the year.
With the Rams it seems like they are very confident in coaching up players that fit their scheme and have very good football intelligence.