Some things can be kept the same. Part 1.
The same or a near equivalent? Equivalence is in the eye of the beholder. Only you know what your child will see as an acceptable, near-miss, substitution and what will only work if it is exactly the same. The items listed below are just examples. You may want to, and need to, think of others.
Car Seat. If your child currently uses a car seat, they’ll need one for any rental car. Your choice is to rent one as ‘special equipment’ with the car or bring your own from home. Bringing your own gives you the 100% certainty that you have no change. There are two other issues to consider when renting a car seat. Firstly, some rental companies charge a lot of money for “special equipment”. Secondly, they tend to buy these things based upon price. Even if you can work with “different”, it probably won’t be as nice as the one that you have.
In order to get the car seat there you can choose between either taking it as a piece of checked baggage or using it on the plane. If doing the latter, be sure that it has a label that says “This restraint is certified for use in motor vehicles and aircraft”. That means that it meets FAA standards and that the cabin staff will accept it. You should, however, check dimensions and “fit” with the airline ahead of times. Seats vary on any aircraft and only some might fit your particular seat.
Booster Seat. As far as car rentals go, all of the same thoughts apply. The difference is that booster seats aren’t suitable for aircraft since they work with a shoulder strap and the plane only has lap belts. Do check with your airline. Some will take a booster seat as checked baggage and make no charge for it. Most airlines will accept it as one of your carry-on items. They may or may not levy their usual charge for carry-on items, if they operate such a charge.
Car rental. Obviously it isn’t your car and is, therefore, different. However, you can keep the body size and type the same. If you drive a compact car at home, a full-size SUV may be a bad rental choice. Similarly, if you drive a large SUV at home, a compact clearly isn’t the same.
It may be worth checking out National Car Rental at your destination. For many of their locations they operate a system where you rent the category but can self-select from any in a line of vehicles in that category. If you are lucky, you may find something that is a reasonable match for your car (but this isn’t guaranteed).