Same tile in kitchen and bathroom. We have a beautiful tile that we used on the walls for a bathroom renovation last year. Add a ceramic tile facing and protect your kitchen island or bar while also adding a unique decorative element that can coordinate or contrast with your backsplash and floor tile. So a different smaller tile would be better. If the bathroom and kitchen floor flowed together then the same tile would be fine.
Choosing the right type is not as simple and going into a store and picking the most attractive or affordable design. In a bathroom you will need something that can stand frequent cleaning possibly including harsh chemicals such as bleach. But it looks like the bath is on a different level the the kitchen. I think it certainly makes sense in the kitchen and laundry as one flows into the other and there is no reason why you cant use the same in the bathroom. We always use the same tile on both the floor and walls as we feel it flows better and gives a greater sense of space. Both kitchen and bathroom have tiles almost of same but with little differences.
Most of the people tend to use the same tiles at both areas. Lo and behold we have almost enough of the bathroom tile left over to do our backsplash. You might want to call this option a foot backsplash Your kitchen island or bar receives constant kicking and bumps from barstools. But it looks like the bath is on a different level the the kitchen. 600mm x 600mm and a smaller tile on the wall eg. But did you know theres a difference between the tiles you should use in your kitchen and those for your bathroom. But it looks like the bath is on a different level the the kitchen.