Celebrity Cruise lines is owned by the parent company Royal Caribbean Cruises Limited. They own both the brands Royal Caribbean International (the cruise line), and Celebrity Cruise Lines. Celebrity is one of my favorite. They are a Premium cruise line. Royal Caribbean is mass market. Celebrity has a more refined experience. They are noted for their service and food.
I sailed on the Summit in Alaska and enjoyed the ship. To compare the Summit to the Explorer is hard to do because they are two totally different classes of ship. You will have to ask yourself what it was you enjoyed about the Explorer. The Summit has activities for children but Royal Caribbean offers more activities for children. The Enchantment of the Seas is different yet than the Explorer. It is an older much smaller ship. It does have rock climbing and a bungee trampoline. Bermuda is a great island with lots of activities.
You should talk with a cruise oriented Travel Agent that can explain the differences more in detail. Other cruise lines like Carnival and NCL may be good fits for you also.