Say in a Texas Hold'em game lower stake is $1, upper stake $2, min buy in $40, max buy in $200. What these values mean & what is their correlation?
So typically people don't refer to the blinds as stakes, however it's technically still correct. Normally when people stake in poker it has connotations of being connected to a backer (i.e. someone giving the player funds to play).
Anyway in the context at what you've posted:
Lower stake - More common to see people refer to the this as the small blind(SB). This is the amount the player to the left of the dealer button must put in to play.
Upper stake - Again more commonly called the big blind(BB). This is the amount the player to the left of the small blind must put in to play.
Min buy-in - This means that is the smallest amount of money you need to sit and play at that table. So if the min buy-in is 40$ and you have 39$ you can't sit and play, you don't have enough.
Max buy-in - This is the max allowed for you to buy-in with. A lot of games are uncapped, meaning there is no max buy-in. Again as an example let's say the max is 200$ and you want to see with 300$ you'll only be allowed sit with 200$. Typically max buy-in games are done so you can't have someone new join the table and buy-in for more than anyone else at the table.