All three of mine were very much planned, but from what you wrote, it sounds like it could just be a "second child" thing. I definitely paid less attention to number two than number one (they were two years apart), A. because I already had an older child to watch who was into everything and B. because I learned that taking a "tumble" likely won't kill them, nor will eating off the floor, climbing on the bed or any of the other things. I think second time moms tend to relax a bit in general, so maybe what you are doing isn't so much caring less but just being more comfortable?
As for "pawning him off" as you put it, I definitely did that more. My oldest never met a babysitter until he was about 18 months. Middle started going to the gym daycare at 8 weeks and had a Saturday babysitter from the time he could have baby food. I think with two that young, you need more breaks.
Not trying to dismiss your concerns, just trying to make you feel better that maybe this isn't a subconscious way of treating them differently but a normal part of being a mom of two.
My second son was a surprise and was born when my first was only 17 months old--I was not ready for that! Going through morning sickness while parenting an 8 month old was no fun at all. But we tried really hard for my first and so being spontaneously pregnant really felt like a blessing. Even though it wasn't under the ideal circumstances. However, I do feel differently towards my ds2. He had 9 hour per day screaming colic until he was two months old...that on top of parenting an 18 month old was difficult. He was a horrible sleeper and cried when he was awake. I felt like all I did was hold a crying baby or a sleeping baby. I got really resentful towards this grouchy little creature. It was not the love at first moment thing I had with ds1. It has taken a long time to let go of the negative reaction I had to his crying. He has a more difficult temperament anyhow, and we clash. BUT, he is about to turn 3 and I adore him. My boys are so different and I appreciate them in different ways. I really had to practice finding the awesome qualities of my 2nd son, because he is completely different from my fantastic 1st son, but now--even though he's difficult sometimes, he is also amazingly sweet and adorable. I think when you have a great first child that you adore, unless your second child is a clone, you have to really work at appreciating the different ways each child is amazing.
All that said, I do parent him differently because he is a second child--as referenced in the above post.