"Starter" is intended for young chicks, generally newly hatched to around 8 weeks of age. "Grower" is intended for chicks in the middle bracket, from around 8 weeks to 16-18ish, or the point of lay. This is all generalized, each brand has it's own instructions so if you really can't decide what to do, go by the bag's recommendations. But there's no rule that you have to switch off of starter, or that you can't feed grower for life.
Don't worry about the name. The things to look at mainly are protein %, calcium %, and size of the feed pieces (as very young or small chicks can struggle with larger pellets for example). Protein for starters are generally around 20% or so, grower may be a little lower. Calcium in both should be around 1% or so. For this reason all flock is often an acceptable substitute for one or both as it hits those numbers.