What does industry * year fixed effect mean?
$Industry \cdot year$ fixed effect is just an interaction term between industry and dummy year variables. For example, you can have dummy particular industry, let us say finance where $D=1$ if firm is a finance firm and $0$ otherwise, then you can have a year dummy which will be set to equal $1$ for particular year and $0$ otherwise. Note typically you will have a dummies to cover industries in your sample and every year, I just used one industry and one year as an example.
$Industry \cdot year$ Is just multiplication of the two dummies, so you end up with third dummy that will be equal to $1$ only if data point is from both that particular industry and year. So it will tell you what "special" effect the industry and year had on the regressand. The effect of this dummy will be amalgamation of effects of unobserved covariates on the regressand.
What are the difference between (firms fixed effect and industry fixed effects) and ( firms fixed effects and industry * year fixed effect)?
firms fixed effect - it is a firm specific dummy that will tell you what unique effect firm specific and time invariant unobservables are having on the regressand.
industry fixed effect - as above but this tell you the effect of industry specific and time invariant unobservables on the regressand.
firms fixed effects and industry * year fixed effect - this was already covered in the first part, but to recap it tells you the specific effect firm or industry in combination with specific year has on the regressand.
Are they all called two-way fixed effects in general?
We talk about 2 way fixed effects when we use both spatial and temporal fixed effects. So when you use firm and year fixed effects you are talking about two way fixed effects. However, note when we talk about two way fixed effects there should actually be two sets of fixed effects not just some interaction like $industry \cdot time$ (see discussion in Imai & Kim 2020). But if you read the paper you linked in most regression tables they have separate firm fixed effects and year fixed effects. This being said the terminology might not always be used consistently in the applied work.