Not in my admittedly quite limited experience. I speak to my mum maybe 2/3 times a week via WhatsApp messages, with the occasional visit and even more occasional phonecall (the last one lasted nearly two hours as she doesn't stop talking). We get on well but certainly don't live in each other's pocket. She'll give me a hand if I need it and I'll help her out too if needed.
Dp on the other hand calls his mum on the way home from five days a week and another call at the weekend. Before lockdown would regularly visit (probably once a fortnight), and does most of her gardening and diy.
He also very firmly put her in her place when she acted like a total bell end towards me after ds was born, so he's not a mummy's boy as such. He has decent boundaries but is close to her.
My own mum much preferred her mil to her mum, understandably so.
My dad's mum was a lovely, kind, intelligent and non violent woman, who never laid a finger on any of her six children (despite it perfectly acceptable to do so at the time), didn't judge anyone, and welcomed my mum like one of her own despite being Irish Catholic and my mum being CofE. My parents are divorced now and have been for nearly 20 years but my mum was at the funeral of both my grandparents on my dad's side, and is often invited to things like birthdays and Christmas, because she and that side of my family get on so well.
My granny on my mum's side would be drunk when my mum came home from school at 3pm, would hit her with belts and slippers, told her and her sisters that their step father was her number one priority, nearly broke my mum's wrist, tried to invite a whole host of relatives my mum didn't know to her wedding (which would have meant her best friend wouldn't have had a space) and was generally pretty awful, judgemental, selfish and dramatic. I've been on the receiving end of this too from time to as an adult, and a great deal less respect for her now than I did as a child. My mum has put strong boundaries up now so takes less of her crap than she used to but she still bullies my aunts, calling them up drunk at 11 at night crying that she wants to be with her dead husband (he died 25 years ago).
I think it really depends on how you behave, as well as myriad other factors, that determines how close mothers are to their adult children, and gender has very little to do with it.