hamburgisch
Hamburg
Relating to the city or federal state of Hamburg, originating from there, or characteristic of it.
Der hamburgische Senat hat ein neues Gesetz beschlossen.
The Hamburg Senate has passed a new law.

Hamburg / Hamburgian
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Hamburg
Relating to the city or federal state of Hamburg, originating from there, or characteristic of it.
Der hamburgische Senat hat ein neues Gesetz beschlossen.
The Hamburg Senate has passed a new law.

The adjective 'hamburgisch' (Hamburg / Hamburgian) is derived from the city name 'Hamburg' with the suffix '-isch' (-ish). This pattern is used with many German cities and regions to express belonging or association.
Das ist ein typisch hamburgisches Schmuddelwetter.
That is typical Hamburg drizzly weather.
Like other adjectives, 'hamburgisch' (Hamburg / Hamburgian) can stand before a noun and is then declined. It can also stand after the noun or verb without declension to describe a characteristic.
Wir besuchen den hamburgischen Hafen.
We are visiting the Hamburg harbor.
You can tell from context whether general origin or the dialect is meant. When it is about language, words like 'Akzent' (accent), 'Dialekt' (dialect), or 'sprechen' (to speak) are often nearby.
Er spricht fließend hamburgisch.
He speaks fluent Hamburg dialect.
In its general meaning, 'hamburgisch' (Hamburg / Hamburgian) is often combined with things the city is known for. Examples are 'der hamburgische Hafen' (the Hamburg harbor), 'das hamburgische Wetter' (Hamburg weather), or 'ein hamburgisches Unternehmen' (a Hamburg company).
Viele hamburgische Reedereien sind international tätig.
Many Hamburg shipping companies operate internationally.
northern German
'norddeutsch' and 'hamburgisch' can both describe something from northern Germany. However, 'norddeutsch' is much broader and can refer to the whole region of northern Germany, its culture, landscape, or way of speaking. 'Hamburgisch' is more specific and refers directly to Hamburg or the typical language and manner of Hamburg. The words can be confused because Hamburg is in northern Germany. When you are speaking generally about the north, 'norddeutsch' fits. When it is really about Hamburg, 'hamburgisch' is more precise.

In dem Lied hört man einige hamburgische Ausdrücke.
You can hear several Hamburg expressions in the song.
Der trockene Humor meines Kollegen wirkt auf viele typisch norddeutsch.
My colleague's dry humor seems typically northern German to many people.