There are some important differences in the various concepts around responsible tourism. Perhaps the best way to understand this is to tell the story of their evolution...
About 30 years across wildlife tourists and wildlife tourism operators began to be concerned that their visits to watch wildlife might be actively contributing to its decline through negative environmental impacts. This wasn't a great thought for them, and they began to advocate the idea of 'leaving no trace or not footprints.' This became better known as ecotourism. Although some people have laid claim to coining the term ecotourism it emerged from different parts of the world around the same time.
Problems with eco tourism
Over the next decade one group of people began to get quite angry about this concept. These people were local communities living alongside the wildlife. They felt that if they were to set aside some of the best areas in their local area for (often) overseas visitors then they too should benefit. These local communities face the 'opportunity cost' of not, for example, using these areas themselves or chopping down trees and taking firewood if an area is to be conserved for wildlife. These, sometimes, poor people cannot afford to do this without some from of compensation from tourism. Lord Marshall, then Chairman of British Airways said the 'we must remember that tourism is essentially the renting out of other people's environments.'
As the years went by ecotourism became an increasingly popular from of marketing and sadly abused by green washers, who exploited its marketing potential without addressing any of the conservation or community issues. In short, there was insufficient focus on the impacts of tourism.
Responsible travel and tourism
Responsible tourism emerged as a solution to both this problem, and the belief that the idea that solutions needed to be found across the wider tourism industry and not just the nature based tourism sector through ecotourism. Responsible travel and tourism acknowledges two important things. Firstly, that the impacts of tourism are cultural and economic as well as environmental. Secondly, that the tourists and the tourism industry must take responsibility for their impacts. Initial responsible tourism definitions tended to focus around maximising the positive social, economic and environmental impacts and minimising the negative ones. A better one comes from the Cape Town Declaration which described responsible tourism as 'creating better places to live in and to visit.' Note how the benefits to local people are central to this idea. I'd perhaps add the word 'authentic' to responsible tourism definitions.
Sustainable travel and tourism are terms that sometimes used, however far less so by the industry than responsible travel and tourism. Sustainability is (an often vague) aspiration, whereas responsible tourism (taking responsibility for the impacts of tourism) is more of a strategy to achieve ambitions of sustainability. Others feel that true sustainability is never achievable, not least due to the CO2 impacts of aviation, and that responsibility for tourism's impacts is more appropriate. It's certainly easier to talk to tourists about acting responsibly.