Yes, there is a difference.
We would use 'admirable' for something that you admire or respect. For example, "I think it's admirable that you set aside an hour a day to exercise! I could never do that."
"It's admirable how she takes care of her elderly parents."
"Laudable' = deserving praise. So the second sentence above, you could use 'laudable' (but I would not use it with the first).
"laudable' is more 'noble' and more praiseworthy than just 'admirable.'
"Cutting the poverty level in half" or "fair and equal housing for everyone" are laudable goals. (these are good causes worthy of praise)