The Arabic word ilah is the counterpart of the English word god. Both mean the thing or entity being worshipped. The Persian khuda, the Latin deus, and the Turkish tanri have similar meaning and connotations.
God, with a capital G, is not an exact equivalent of the term Allah, although we use it for practical reasons throughout this book. Rather, it is closer to the Islamic conception of ilah. In Arabic, Allah is the essential personal name of God and comprises all His Beautiful Names (asma' al-husna). When Allah is said, the One, the Supreme Being, the Creator, the Owner, the Sustainer, the All-Powerful, the All-Knowing, the All-Encompassing, whose Names and Attributes are manifested in creation, comes to mind. This term also refers to His absolute Oneness as well as His having no defect or partner. The word God, as used by non-Muslims, contains various conceptions and connotations that Muslims cannot accept. 
As Allah is a proper name peculiar to the One Supreme Being, we say la ilaha illa Allah (there is no god but Allah) instead of la Allah illa Allah. By saying la ilaha illa Allah, we first deny all non-deities and then affirm the One known by the name Allah. In other words, only Allah is Allah, and only He is worthy of worship.
 For example, the Christian concept of Jesus as God or the "son" of God. Of course, we should make an effort to understand what people mean when they use such ambiguous terms.