Sounds like they did germinate, at least some of them, David. Unless some weed seeds blew in there or something. Got a picture?
You can tell them apart by the shapes of the leaves - carrots will have feathery little leaves, spinach will be dark green, long and narrow and radish are round (I think . . ). Unless it's a very large planter, you've got a job ahead of you to thin out those seedlings into other planters. Each plant needs about 4in. square to grow to maturity. Carrots need deep, airy soil unless it is a short-rooted type.