Two members swap at the same time i.e "you stay at mine while I stay at yours".
Non-simultaneous home exchange
Two members swap homes but at different times eg you stay at mine at Easter and I'll come to you in the summer. This works well with second homes or when you know that your home will be empty. The increased flexibility over dates can increase your options.
You host another member in your home for a few days while you are there. This is not always reciprocated, but is a nice way to meet new people. The guests do not pay, but it's customary for them to take their hosts out to dinner or something similar.
You can either request a homesit or offer yourself as a home-sitter. Home-sitters often look after plants and pets. Be clear about who pays for what before finalising arrangements.
A Youth Exchange can involve two teenagers staying with each other's families at different times - often to improve their language skills. Sometimes a family might offer use of their holiday home in return for hosting their teenager.