Tension and compression generally come together when we are talking about materials carrying loads. it will be better to explain this using the knowledge about internal bonds between atoms. For example, when you stand on a wood ladder, the top of the wood piece you are standing on is under compression, and the atoms along the top of that wood piece are pushed together, compressing the interatomic bonds along the wood piece. At the same time, the atoms along the bottom of that wood piece are pulled apart, causing the inter-atomic bonds to stretch. The bottom of that wood piece is under tension. However, not all material handle tension and compression the same way. Some materials, like steel, supports tension better than other materials. So the suspension cables in bridges are made of thousands of steel strings. Concrete supports compression better than other things so we use them on foundations of tall buildings. The choice of material is quite complicated, tension and compression are just two of those many factors physicists and architects have to deal with.