There are considerable grammatical differences. Hungarian is an Agglutinative language: what words do and mean in a sentence is affected by the bits that are added on, before, after and within them.

A Basic Outline of Hungarian Grammar

Articles

The word for 'the' is 'a' apart from words beginning with a consonant when it is 'az'.

So 'the table' is 'az asztal' but 'the flat' is 'a lakás'.

The word for 'a' is 'egy' so 'a table'  is 'egy asztal'.

This can be seen in 'I'd like to book a table for two.'  which is 'Szeretnék egy asztalt foglalni két személyre '.

Hungarian definite and indefinite articles do not change when in the plural as do some European languages (E.g. In Spanish 'el perro'  (the dog) becomes 'los perros'  (the dogs) when referring to more than one.

Nouns

Nouns in Hungarian have a complicated system of Inflected endings. Learning Phrases is a simple way to start to communicate in Hungarian as you can avoid learning these rules.

Inflection is the modification of a word to alter its grammatical function, and in Hungarian nouns the modification is made to the noun ending by adding layer of suffixes.
The distinction between singular and plural Hungarian nouns is used to illustrate inflection in Hungarian:

könyv (book)     becomes könyek (books)
kalap (hat)        becomes kalapok (hats)

The text in bold is the prefix used to show number (singular or plural) and is here either ek or ok. The prefix depends on the noun and Hungarian rules of vowel harmony.

Hungarian nouns are inflected to show case and possession in addition to singular or plural. The prefex's showing case and possession are added in order to the noun stem:

Noun Stem + Number (singular or plural) + Possessive + Case.

An example showing number, possession and case is:-

az emailj + ei + m + et  my e-mails.

ei is a plural suffix.
m is a suffix indicating possession
et indicates (Accusative).

Nouns do not distinguish between masculine and feminine.

Adjectives in Hungarian

Hungarian adjectives are either Attributive or Predicative.

When used attributively a Hungarian adjective comes before the noun which it describes:

a piros aut ó     a red car
zöld kártya      a green card
nagy ház         a red house.

Adjectives used attributively do not agree with the noun being described (by changing case or number). In contrast, when used predicatively adjectives in Hungarian agree in number with the noun being described.