What is the difference between Geld sparen and Geld zurücklegen?
Don't they both mean save money? When do you use what?
Geld zurücklegen or Geld zur Seite legen would specifically refer to putting money aside, whether it's under a matress or in a bank.
Example
Ich lege für mein Alter Geld zurück.
Translation
I put money aside for my old age.
Or
Ich lege jeden Tag Geld zur Seite, damit ich mir ein neues Auto kaufen kann.
Translation
I put money aside every day, so I can buy a new car.
Geld sparen has that connotation, but also can simply mean that you saved money by spending less, such as shopping somewhere cheaper.
As in the old proverb
Spare [Geld] in der Zeit, dann hast du in der Not.
Translation
Save [money] in times when you can, so you have it when times are rough.
But also in this sense
Wenn ich bei Aldi einkaufe, dann spare ich Geld.
Translation
When I shop at Aldi, I save money.
There is a subtle difference.
(Geld) sparen means that you create an extra bank account or put the money under your pillow (for example to buy something expensive in the future).
Wir sparen für ein neues Auto.
Also, sparen means that you have a possibility to spend less money on something.
Dank dem Sonderangebot konnten wir 100€ sparen, weil das Fahrrad nur 899 € gekostet hat.
Geld zurücklegen has a similar meaning to the first meaning of sparen, but it implies often, that you save money without any specific goal; mostly to have something on the side (auf der hohen Kante) if your financial situation gets worse in the future. But it can mean saving money for a goal. So, this is quite the same meaning as sparen (1st meaning).
Wir haben ein wenig Geld zurückgelegt (=auf die Hohe Kante gelegt), für den Fall, dass wir das Land verlassen müssen.
Wir verdienen gut und sparen.
Deutsche sind Sparer. Sie geben nicht viel aus, sie legen lieber etwas zurück.
Wir haben bereits 6000€ für ein neues Auto zurückgelegt.
Another point is that sparen subliminally implies a specific lifestyle (of being sparsam). If you have a very good salary, you don't have to sparen, but you can still zurücklegen something.
Ich und mein Mann führen eine erfolgreiche Firma. Obwohl wir nicht besonders sparen, konnten wir bereits eine schöne Summe für ein Haus zurücklegen.
There is a slight difference between the two expressions:
Geld sparen
Is used for different purposes:
Mein Bruder spart auf ein neues Auto
Sparen Sie bares Geld - Kaufen Sie Woopy im 10er-Pack!
Geld zurücklegen
Only has the former meaning, there is always some "grand purpose" behind the saving (not necessarily excluding the "grand purpose" of just owning the money):
Wir legen heute schon jeden Monat Geld für unsere Altersversorgung zurück
Geld sparen is somewhat redundant, since sparen alone already means to save money. It is only to due the inflationary use in advertisements (where it frequently indicates just spending a [very little] bit less), that additional clarification is useful.
Geld zurücklegen already implies putting the money into a separate bank account or just in an envelope, so it won't be spent easily.
In my opinion as a native speaker, "Geld sparen" refers to saving money in general maybe without a special purpose. I would always use "Zurücklegen" with something specific in mind why I put this money aside. So, the difference is not the location where you put it, but why you put it there.