Breaking and Entering
Similar to burglary, it is a fifth degree felony to unlawfully enter a nonresidential structure (or surrounding land) in or on which no one (other than an accomplice) was present, with the intent of committing a crime therein. (Oh. Rev. Code Ann. § 2911.13.)
This is a less serious offense than burglary because it involves a structure that is both unoccupied and nonresidential (such as an abandoned warehouse), two attributes that otherwise increase the likelihood of terror or harm to potential victims.
Trespass
Similar to burglary, trespass is defined as knowingly entering onto private property without the authority to do so. The difference between the two crimes is that trespass does not have the second element explained above (intending to commit another crime inside). Instead, merely entering qualifies as trespass.
Trespass is broken into two categories (in addition to aggravated trespass, described in the next section).
Trespass onto land is a fourth degree misdemeanor, and includes knowingly entering or remaining on private property without authority to do so. As this definition implies, the defendant must have had notice that the land was private, which may be given in several ways. Some examples include conspicuously posted signs (such as those reading “No Trespassing” or “Private Property”), actual communication from the property owner or an agent (such as a security guard), or other obvious indicators of private property such as fences or gates. (Oh. Rev. Code Ann. § 2911.21.)
Trespass into a dwelling is a fourth degree felony, and includes entering a dwelling without permission when someone (other than an accomplice) is likely to be present in that dwelling. (Oh. Rev. Code Ann. § 2911.12(B).)
Aggravated Trespass
Aggravated trespass is a first degree misdemeanor, and includes entering or remaining on private land or premises without permission, with the purpose of committing some misdemeanor involving actual or threatened physical harm to another while there.
Unlike the forms of trespass described above, aggravated trespass (like burglary) has both the “entry” and “intention to commit a crime inside” elements. But it is a lesser crime than burglary because it only involves entry onto land, and because the intended crime is a misdemeanor (not a felony, as with burglary).
(Oh. Rev. Code Ann. § 2911.211.)
Source: http://www.criminaldefenselawyer.com/resources/burglary-and-home-invasions-ohio.htm#