Anti-Science: Anti-science is about being anti-scientific method, the process that requires evidence etc. These people do not consider the scientific method as a way of verifying claims or approaching the truth. They think that some questions are beyond the scientific method.
The best example is a section of those who believe in God. When asked about the evidence for God, they respond - Does everything need to require evidence? Some are about faith, they are beyond science.
This is anti-science because it disregards the scientific method altogether.
Pseudoscience: Using science terminology but not the scientific method to justify certain things, mostly woo-woo.
For instance, if someone claims that eclipses cause disturbances in mental health because the change in gravity affects the fluids in the brain, it's pseudoscience. It's using science terms without scientific method - it neither gives a mathematical calculation of the amount of fluid disturbance that's big enough to cause a disturbance (also a mechanism that translates fluid disturbance to alteration of mental status) nor does it provide experimental proof.
Most modern age godmen propagate pseudoscience. They give the legitimacy of science to their claims by using science terms without the following scientific method. It is aimed to convince people who do not want to be seen as being anti-science.
Science denial: Denying science completely but on flimsy reasons. Anti vaxers and Anti-climate change people come under this category.
Despite enormous documented evidence on vaccines and climate change, science deniers hold on to flimsy reasons to deny it. Some anti vaxers, for instance, say: Why did I not get the disease despite not being vaccinated? This is a corporate scam.
Some of it can also be due to a misunderstanding of the scientific method. A great example is that of Phoebe in the famous sitcom FRIENDS, denying evolution saying - if there's a tiny probability that evolution could be wrong, then why should I believe it.
The difference between science deniers and anti-science is that anti-science people deny the approach of scientific method altogether. Science deniers, on the other hand, claim to follow scientific method but either misinterpret it or find flimsiest objections to scientifically proven claims.