For me the difference is one of the order of priortization and planning - effectively, and motivation as well though I am not questioning that these women mean well.
Someone who wishes to offer assistance to folks who are ill can become a doctor, nurse, therapist or may volunteer to participate in "meals on wheels". Any of those choices and pursuits may stem from similar desires to help, but require different personal commitments, training, tools and funding. No one would suggest that an individual's desire to help, where the individual is able to bring meals, qualifies them to perform functions which requires specific medical training - unless that individual actually obtains the medical training. The motivation to help doesn't negate the need to prepare appropriately, which also requires motivation.
An established charity - and donations to same - may well involve funding travel and other costs, but would generally do so in the context of weighing the benefits against the cost.
These girls seem to be asking for funding to pursue a particular choice, which while well meant, has had negligible consideration of cost/benefit in terms of meeting the charitable aim "to do good" first. Their charitable thought is tied, by them, to a personal interest in going to a particular location. Rather than pursuing an involvement with an organization with which they could volunteer, or be hired by - which could be chosen based on where they would be located - their current course puts their "desired course of action" ahead of, or at least on equal footing with "achieving benefit" to others.
And pursuing their course is fine, if they do so independently, but asking others to fund it does - I think - ask others to fund their personal choice differently than donations to an organization which may pay for travel of its employees or volunteers. The difference - to me - is that it is entirely their choice how/what/cost for their endeavor may be without outside accountability versus joining or affiliating with an organized effort, and making commitments to anyone other than themself as to how to proceed to implement good intentions.