Longtermism and effective altruism are two different ideas which are sometimes but not always held by the same people, so whatever you think about them, I suggest thinking about them separately.
Briefly: effective altruism is about doing the most good you can with your donations. If you want to save human lives, then donating to effective anti-malaria charities in sub-Saharan Africa will go a lot further than donating to an anti-poverty charity in the US, for example. If you care about climate change, then the effective altruist approach would be to donate to the projects that get the maximum possible reduction in CO2 for your buck. Givewell is the most prominent example of an organisation following this approach.
Obviously, there are extensive technical debates about what counts as the best thing to do. For example, if you donate money to an anti-malaria charity that hands out bed-nets now, you can save a reasonably quantifiable number of lives. If you donate money to an organisation that is researching a malaria vaccine, you have some chance of saving a lot more lives (if the vaccine works) and some chance of wasting it. And doing work to mitigate potential future pandemics that haven’t happened yet, like trying to invent an Ebola vaccine, is another step up in potentially-huge-but-hard-to-quantify. So there is a debate about how to think about that and different individuals within the effective altruist movement will have different takes on what is the ‘best’ thing to do. Some effective altruists do focus on trying to prevent/mitigate climate change, but a majority tend to focus on health and anti-poverty measures in developing countries.
As I understand it, ‘long-termism’ is an umbrella term for people who believe we should take long-term consequences and futures seriously. They generally believe that we owe future people the same moral consideration as we owe people who are alive today. So long-termists care a lot about preventing major future catastrophes, including runaway climate change, and are especially focused on the risk of human extinction, be it from climate change, nuclear war, or rogue AI, or some other event. The long-termist argument is that preventing extinction or failure of civilisation doesn’t just save the people who are alive at the time of the extinction event, it saves all future people who would have existed if human civilisation kept going, which is an incomparably larger number. (I am trying to do my best to summarise the long-termist view, but it isn’t my personal view, so I hope I’m not getting it too wrong.)
Effective altruists generally want to spend money on saving/improving the most human lives (although there is a live debate about how much weight people should put on animal welfare vs human welfare). If an effective altruist is also a long-termist, they generally conclude that preventing even small risks of extinction is better than anything else they can do with their money. It’s a clear strain of thought within the effective altruist movement, but I don’t think it’s a majority, and you can certainly be an effective altruist without being a long-termist. You just have to care about actually doing good with your money. Not being seen to do good, not getting kudos for following the latest fashionable cause, not getting your name on a fancy building, but care about actually helping people. Or climate, or animals, or whatever it is you want to help.