Your pitch to different funders should vary somewhat, but you should not change your core values and accomplishments to meet the interests of your funders. You need to know and communicate to all possible funders your mission, what you are good at, and how you are serving the public. You don’t want to be pulled wildly one way because there is funding there and then wildly another way because there is different funding next year.
Nevertheless, your mission and work will probably have different aspects that you can emphasize when talking to prospective funders. Finding out what in your work excites or resonates with your perspective donors should shape your funding pitch. Suppose a news organization’s core mission is to cover environmental issues. Communicating with a journalism foundation about what in that work is important to them might be quite different than what’s said to an organization that wants to build public awareness of an environmental issue. Your pitch will vary with institutional donors depending on their needs and what they hope your work will accomplish.
Individual donors also have different interests in what you are doing. One might really love reporters, think they are doing heroic work, and want to support good journalism. Another might be motivated by a desire to have community members become well-informed voters. Both those individuals may support you, but your conversations with them should be different, reflecting what in your work appeals to them. The first conversation might be a behind-the-scenes look at who your reporters are and how they covered a story. The second conversation would focus on stories that had never been told before, the extent of readership, and the civic impact of the journalism.