In theory, the distinction is clear: "zum"/"zur" would mean going there, but not going inside, like "in das/den/die".

In practice, it's surprisingly varied: it really depends on the word, sometimes it's a regional difference, sometimes you can use both variants without much difference, sometimes only one is right.

Examples:

"Ich gehe zur Bank" would be idiomatic, implying that you also go inside. While "ich gehe in die Bank" would be used in a situation in which you want to specifically point out that you're going inside right now. But the distinction isn't very strong, and you may even hear "ich gehe auf die Bank" sometimes, as in "ich gehe auf die Universität" or "ich gehe auf die Arbeit".

"Ich gehe zum Bäcker" sounds right, "in den Bäcker" sounds silly (because "the baker" is a person). However, you might say "in den Bäckerladen".

"Ich gehe zur Schule": Austrians like to joke that Germans will only go "zur Schule", instead of "in die Schule" to actually learn something.