The main difference between the terms "synagogue," "temple" and the related "shul" is the tradition and intent of the person using the term. Any of the three names can be applied to a place of worship in the Jewish faith, but some terms are preferred over others by different groups for various reasons.
In Hebrew, the structure in which a congregation meets for worship services is called a "Beit K'nesset." This translates as "place of assembly." The Hebrew term isn't commonly used among English speakers. Orthodox and Hasidic believers sometimes use the word "shul" to describe their place of worship. This word is Yiddish and derives from the German "schule," meaning school. Its use is a clue to the educational role Orthodox Jews see for their religious services.
"Synagogue" is derived from the Greek translation of Beit K'nesset, and is fairly neutral. The word is favored by Conservative Jews as a faithful translation of the original Hebrew term, and it is commonly used across sectarian boundaries as a compromise between Orthodox and Reform traditions.
"Temple" is a word commonly used by Reform Jews. Referring to a site as a temple expresses the largely Reform opinion that any place Jews practice their faith is the equal of the Temple of Jerusalem. This has the potential to offend some Orthodox believers, further encouraging use of the all-purpose word "synagogue."