What is the difference between multi-task lasso regression and ridge regression? The optimization function of multi-task lasso regression is

$mi{n}_{w}\sum _{l=1}^{L}1/{N}_{t}\sum _{i=1}^{{N}_{t}}{J}^{l}(w,x,y)+\gamma \sum _{l=1}^{L}||{w}^{l}|{|}_{2}$

while ridge regression is

$mi{n}_{w}\sum _{l=1}^{L}1/{N}_{t}{J}^{l}(w,x,y)+\gamma ||{w}^{l}|{|}_{2}$

which looks the same as the ridge regression. As for me, the problem of multi-task lasso regression is equivalent to solve global ridge regression. So what is the difference between these two regression methods? Both of them use ${L}_{2}$ function. Or does it mean that in multi-task lasso regression, the shape of $W$ is (1,n)?

$mi{n}_{w}\sum _{l=1}^{L}1/{N}_{t}\sum _{i=1}^{{N}_{t}}{J}^{l}(w,x,y)+\gamma \sum _{l=1}^{L}||{w}^{l}|{|}_{2}$

while ridge regression is

$mi{n}_{w}\sum _{l=1}^{L}1/{N}_{t}{J}^{l}(w,x,y)+\gamma ||{w}^{l}|{|}_{2}$

which looks the same as the ridge regression. As for me, the problem of multi-task lasso regression is equivalent to solve global ridge regression. So what is the difference between these two regression methods? Both of them use ${L}_{2}$ function. Or does it mean that in multi-task lasso regression, the shape of $W$ is (1,n)?