"Are charitable donations a form of taxes?" is also the wrong question.
The answer to both is "no." This rather misses the point.
If "we" are the people, and the government is to further the goals of the people in some societally useful and beneficial way, then taxes further the goals of the people. It should be for the general welfare and common good. Keep in mind that "general welfare" is the happiness, prosperity, and "doing well" of the population as a whole.
But the government can't express the ideals of all the people. Nor can it know the people's mind. Because, in fact, ultimately the government is a group of people paid by taxes. Any time you get a group of people working as a group they will develop their own idea about what's good and proper. Put them in power and before long they know what you want and need better than you do--and, oddly, that'll be exactly what they believed was wanted and needed all along.
So the government has allowed for personal sponsoring of societally good and useful things, things that promote the general welfare and common good, even if locally, things that are an expression of popular will with social consequences. Religious and cultural and "social welfare" and educational organizations, for example, have blurry lines. The church I was in engaged in social welfare work, to a limited extent. It also engaged in cultural activities. It was part of civil society, and the US government has traditionally not been so self-centric as to disallow sponsoring of these activities.
So charitable contributions and taxes aren't equivalent. One goes for activities as authorized by politicians and bureaucrats, the former ostensibly representing us in general but only with difficulty representing all of us at any time or even most of us on a particular issue. The other goes for activities deemed important by individuals.
But charitable contributions and taxes are equivalent. Both go for activities deemed by at least some to be societally useful and beneficial, if not essential. Both constitute a sacrifice--whether compelled or voluntary--on behalf of what is deemed the common good and general welfare.