modisch
fashionable
In line with current fashion; following the latest trend.
Er kaufte sich eine neue, sehr modische Sonnenbrille.
He bought himself a new, very fashionable pair of sunglasses.

fashionable
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fashionable
In line with current fashion; following the latest trend.
Er kaufte sich eine neue, sehr modische Sonnenbrille.
He bought himself a new, very fashionable pair of sunglasses.

The adjective 'modisch' (fashionable) is derived directly from the noun 'die Mode' (fashion). The ending '-isch' is often used to form an adjective from a noun.
Sie interessiert sich sehr für die aktuelle Mode und trägt immer modische Kleidung.
She is very interested in current fashion and always wears fashionable clothing.
'Modisch' (fashionable/fashionably) can describe not only a noun, but can also be used as an adverb to modify a verb. It is especially common in combination with verbs such as 'sich kleiden' (to dress) or 'aussehen' (to look).
Er kleidet sich immer sehr modisch und elegant.
He always dresses very fashionably and elegantly.
'Modisch' (fashionable) often describes things that people wear or that belong to personal style. Typical combinations are: modische Kleidung (fashionable clothing), ein modischer Haarschnitt (a fashionable haircut), eine modische Brille (fashionable glasses), or modische Schuhe (fashionable shoes).
Für den Sommer sucht sie noch eine modische Sonnenbrille.
For the summer, she is still looking for a fashionable pair of sunglasses.
modern
'modern' and 'modisch' can both mean that something seems current. That is why they are easy to confuse. 'modern' is broader: it fits technology, apartments, buildings, ideas, or ways of working. 'modisch' relates more strongly to fashion and trends, especially with clothing, hairstyles, colors, or style. A laptop is modern, but normally not 'modisch'. A jacket can be 'modisch' because it is currently on trend. As a simple guide: use 'modern' for the present day in general, and 'modisch' for fashion and trends.

Sofia kauft eine modische Jacke, weil sie ihr für die Feier gut gefällt.
Sofia buys a fashionable jacket because she likes it for the party.
Wegen der neuen Küche wirkt die Wohnung jetzt viel moderner.
Because of the new kitchen, the apartment now looks much more modern.