to factor out means: to put a common factor outside parantheses. Given: (6x+4y). We now factor out 2. That leads to 2(3x+2y).

to factorise means: to convert a term into a number of factors, that is terms that are being multiplied one after the other. Given: 60xy (meaning 60 times x times y). This can be factorised as 2*3*10*x*y.