army / host
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army
The land forces of a state, that is, the part of the military that fights on the ground. It is one branch of the armed forces alongside the navy and air force.
Nach der Schule ging er für zwei Jahre zum Heer.
After school, he joined the army for two years.
The military meaning can be recognized from the context of state, defense, or soldiers. The figurative meaning of a large number is almost always made clear by the structure `ein Heer von + [plural noun]` (a host/army of + plural noun).
Das Heer des Landes besteht aus Berufssoldaten.
The country's army consists of professional soldiers.
In a military context, there are fixed expressions. Common ones are `zum Heer gehen` (to join the army) and `beim Heer dienen` (to serve in the army).
Er musste nach der Schule für den Wehrdienst zum Heer.
After school, he had to join the army for military service.
The use of 'Heer' (host/army) for a crowd of people is a metaphor. It is often used in the press or literature to create an impressive image of a large, moving group.
Ein ganzes Heer von Reportern belagerte den Eingang.
A whole host of reporters besieged the entrance.
amount / crowd
'die Menge' and 'das Heer' can both mean a large number of people, animals, or things. 'die Menge' is the normal, neutral word and fits very many everyday situations. It can also simply mean a quantity, not necessarily a huge one. In this relation, 'das Heer' means a very large, almost overwhelming collection and sounds more figurative. For example, people say 'ein Heer von Helfern' (a host of helpers) or 'ein Heer von Fragen' (a host of questions). The words can be confused because both can express a large number. In everyday language, 'Menge' is usually safer; use 'Heer' when you want to emphasize the size especially strongly.
Nach der Ankündigung hatte das Büro ein Heer von Anrufen zu beantworten.
After the announcement, the office had a host of calls to answer.
Vor dem Stadion wartete eine große Menge auf den Einlass.
A large crowd waited in front of the stadium to be let in.