What’s the difference between entrance and entry?

If you are looking a these words as nouns, they essentially mean the same thing. The difference is that an entrance tends to imply something physical, like a door, gate or archway. An entry is more abstract and broader in meaning. While it can refer to a physical entrance, it also suggests access, admission, an appearance or a coming.

As a side note, entrance is a homonym. Homonyms are words that are spelled the same and that sound the similar, but that have different meanings. En’-trance can be a noun meaning an opening, like a door, gate or passage way. But en-trance’ can also be a verb that means to fill someone with delight or wonder, so that their attention is taken by something or someone (i.e. enchanted, mesmerized, captivated, spellbound, bewitched).

With the noun, enter (from the french entrer) is the root and the suffix -ance refers to the action, state, or quality of doing something or of being something his sudden appearance (=he appeared suddenly) her brilliance (=she is brilliant).

With the verb, the root is trance (from the Latin transeo “to cross over”, for example change from a state of consciousness to a state of unconsciousness) and the prefix is en- meaning in.