Should i use the same drywall in the bathroom as in the rest of the house?

I recommend using MR (Moisture Resistant) drywall for the bathroom, and possibly for the basement if there are moisture issues. It is not much more expensive, and it can save you a big headache later

MR (Moisture Resistant) drywall? In bathrooms the moisture is on the inside of the room. When drywall is painted, the paint becomes a moisture barrier so the moisture in the bathroom should not reach to the actual drywall wall. As commented above, make sure you have exhaust fans in place that vent the moist air outside. (and not into the attic) If the shower walls are going to be tiled, you should use cement board around the shower walls. Grout lines can crack some times and water will follow the crack to the wall surface. Using drywall in the area will be problems.

In bathrooms I use MR (often called 'Green') only in the tub-shower area even if it's going to be covered with tile or plastic enclosures. Using it in the whole bath really doesn't merit the extra cost. I use a good quality sealer on the regular drywall & a semi-gloss paint to seal it. This is more than enough for the average home.

One of the biggest moisture issues isn't water going down the tub or inside the walls, it's poor or non-existent ventilation. Every bath should have an exhaust fan leading to the outside of the home. Trouble is, most people don't use them & leave the steam to condense & dry on the walls. This won't hurt the drywall but can lead to mold/mildew and water spots on the ceiling & upper walls. If you want to keep the room warm for after your bath/shower put in a good overhead infrared light. Does a much better job & saves future wall washing.

Don't forget exhaust fans need periodic cleaning to keep them working efficiently so when you change your smoke detector batteries, clean the fan, too. Good luck!