Should or Must

Should / must

1)      Should 

Should expresses advisability, a suggestion.  "It is advisable to..."  or "This is a suggestion… " It is weaker than must. 

Should is used to give advice, to make recommendations or to talk about what we think is right or wrong.

e.g. :

You should eat more slowly.

You shouldn't work so much.

People should protect the environment. It makes good sense. 

We should select cars so that they are more fuel-efficient.

We should use re-usable bags when shopping.

2)      must

We use must to express a stronger point of view.  "We need to..."  "We have to..." The modal must also expresses opinion, one person's point of view.

Must is used to talk about an obligation or probability.

Mustn’t is used to forbid something, it is forbidden, it is foolish to do it.

e.g.

You must do your homework.

You mustn't be late.

We must protect our environment, or our resources will disappear.

Engineers must redesign engines so that they are more fuel-efficient.

Stores must give out recyclable plastic bags.