When to use "nude" and when "naked"

Nude is by and large used only to refer to the absence of clothing or any covering in general.

• Nude beaches
• Nude model

Naked, on the other hand, has far wider connotations than nude. You can look them up here.

• Naked eye
• Naked truth
• Naked to one's enemies

It's also worth noting that naked is a rather technical word in life sciences, which is not the case with nude.

The Naked and the Nude

Robert Graves

For me, the naked and the nude
(By lexicographers construed
As synonyms that should express
The same deficiency of dress
Or shelter) stand as wide apart
As love from lies, or truth from art.

Lovers without reproach will gaze
On bodies naked and ablaze;
The Hippocratic eye will see
In nakedness, anatomy;
And naked shines the Goddess when
She mounts her lion among men.

The nude are bold, the nude are sly
To hold each treasonable eye.
While draping by a showman's trick
Their dishabille in rhetoric,
They grin a mock-religious grin
Of scorn at those of naked skin.

The naked, therefore, who compete
Against the nude may know defeat;
Yet when they both together tread
The briary pastures of the dead,
By Gorgons with long whips pursued,
How naked go the sometime nude!