I find it a slightly weird question. It's not as if there's a specific subspecies who are MILs and behave in a certain way, just like 'school mums' aren't some group with group behaviours, they're just female fellow human beings who have children at your child's school. MILs are just women who are of an age to have adult children who are in a longterm relationship with a partner the MIL has some relationship with, too.
I think the IL tensions are purely down to the fact that in most cases, you know and love your parents, and have been dealing with/bearing with their strange peccadilloes since childhood, but you generally meet your PILs in adulthood, they're your partner's parents but not yours, and while your partner has likewise been loving them/dealing with them since childhood, you haven't, and don't have that longterm relationship or semi-biological fondness to fall back on.
For instance, both my mother and my MIL are, in their very different ways, tremendously difficult people -- my mother is a lonely, timid, people-pleaser who defers to everyone (to the point where she just agrees with the last thing anyone has said to her and will nod along silently to racist rants because 'it would be rude' to argue), trots about doing things for others, gets overlooked and unconsciously resents it hugely. My MIL is bossy, tactless and unimaginative, hugely overinvested in being clan matriarch and has absolutely no idea that there are other ways of doing things.
I find MIL far more annoying, purely because my siblings and I are used to our mother's ways, whereas DH (though he's heroic around her) find my mother far more maddening, because he and his siblings are used to his own mother.
I think that's natural enough. We all rub along fine, and I adore FIL, who is a generous and kind-spirited man who has had a difficult life, and decades of ill health, but is still going into prisons as a befriender and spent the last years of his working life doing sterling work in a union.