In really simple words, the semantic field is the study of the meanings of words. When we put words in a web by semantic value, what we are doing is relating the words by what they mean. This is a method often used in concept webs to convey a clearer meaning of something. This is why it is a "semantic" field. The word "semantics" and its Greek sēmantiká has, as a root word, the lexeme "seme" which means "sign".
The lexical field studies the morphology of words, or their shape, form, and construction. When we put together a lexical web, we are relating words that are similar in formation probably because they are also similar in linguistic origins. Hence, when these kinds of lexemes are put together they should have the same structure, and form. The lexical field theory (1931) argued that words are grouped in similar manner by construction do to their cultural and geographical origins. Therefore, the lexical field is not only a study but also a theory in itself.
Hence, they are not the same. Semantics is the study of the meaning of words whereas morphology is the study of the construction of words. One is meaning, and the other one is form.
In short, anything to do with semantics deals with meaning. So, if we ask what is the semantic range of a word, we are asking how that word can be used. In other words, we are talking about the boundaries of that word from a meaning perspective. Also semantics studies synonyms to see what other words have a similar or overlapping meanings.
Lexical fields differs in some way, even if there is overlap. Lexical fields study how words affect other words in a sentence. For example the presence of a certain word can change the whole meaning of another word in a radical sense. The best example that I have come across is the word, "roller coaster." It might seem that the word "roller coaster" has a very limited semantic range, namely what you see in an amusement park. However within the context of a sentence, that word can have a different meaning altogether, because the lexical range changes it.
Here is an example: "My week has been crazy and my emotions are going nuts; my life is a roller coaster."
In short, the lexical field has changed that word. By this example, we can see that the semantic range is limited to the word itself, the lexical range also includes other words in the context.