It's more important that they are informing you of traffic. The make is extra-curricular information that you will, with experience, use to your advantage.
By the same token, never assume anything. It's okay to ask for clarification. There's no embarrassment in doing so, just like making a go-around if a nasty crosswind is testing your limits.
You're not increasing the workload on the controller by asking - they'll be happy you did, as let's face it, the alternative would very much increase their workload...