Beetroot seedlings will look like tiny beetroot leaves with red stems and leeks will look like tiny tiny chives, often with a bent tip, and yes ... you'll recognise them when they appear 
If you have any little plants that have roundish sprawling slightly furry leaves they defiinitely won't be beetroot or leeks so you can pull them up - have you put markers at each end of the rows? If not it's a good idea if you do that next time - gives you a bit of a clue where to look. Things are very slow getting going this year because of the cold weather, my beetroot and carrots are still very tiny and I put them in at the beginning of May, but they'll get going when we get some sunshine for more than 10 minutes at a time - welcome to the joys of gardening 