entwickelt
developed
At a high level of technical, economic, or social development. Often used for countries or industries.
Japan ist ein hoch entwickeltes Industrieland.
Japan is a highly developed industrialized country.

developed
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developed
At a high level of technical, economic, or social development. Often used for countries or industries.
Japan ist ein hoch entwickeltes Industrieland.
Japan is a highly developed industrialized country.

'Entwickelt' (developed) is the past participle of the verb 'entwickeln' (to develop) and is used here as an adjective. It describes a state that is the result of a process of development.
Die Software ist noch nicht voll entwickelt und hat einige Fehler.
The software is not yet fully developed and has some bugs.
The adjective 'entwickelt' (developed) is very often specified more closely by adverbs that indicate the degree of development. Typical combinations are 'hoch entwickelt' (highly developed), 'weit entwickelt' (well advanced), 'gut entwickelt' (well developed), or 'voll entwickelt' (fully developed).
Singapur ist ein wirtschaftlich hoch entwickeltes Land.
Singapore is an economically highly developed country.
In the context of countries or the economy, people often speak of 'hoch entwickelten Industrieländern' (highly developed industrialized countries), 'technisch entwickelten Gesellschaften' (technically developed societies), or a 'gut entwickelten Infrastruktur' (well-developed infrastructure).
Die Region hat eine sehr gut entwickelte Tourismusbranche.
The region has a very well-developed tourism industry.
When 'entwickelt' (developed) describes a person, it refers to intellectual or social maturity. It is often used with the addition 'für sein/ihr Alter' (for his/her age).
Er ist für sein Alter schon sehr weit entwickelt und sehr verantwortungsbewusst.
For his age, he is already very mature and very responsible.
modern
'modern' and 'entwickelt' can both have to do with progress. 'modern' describes something as current or suited to the present day. 'entwickelt' more often describes a high level of development in technology, the economy, or society. The word is often used for countries, regions, or industries. The words can be confused because modern things are often also highly developed. But 'modern' describes the current character of something, while 'entwickelt' describes the level it has reached.

Die Region hat eine gut entwickelte Industrie.
The region has a well-developed industry.
Im Training benutzen wir morgen moderne Geräte.
In training tomorrow, we will use modern equipment.