A bilateral agreement or bilateral contract is an agreement with two parties as opposed to one with more than two parties. It has no real connotations and is strictly a descriptive term
A unilateral contract is a contract proposed by one party on a take it or leave it basis to one or more other parties to accept. Once accepted, it is often simultaneously a unilateral contract and a bilateral contract.
A one-sided contract is a contract whose terms favor one side in an extreme manner to the detriment of another. A unilateral contract could be one-sided, but could also be balanced and fair.
A two-sided contract is a contract whose terms balance the interests of the parties to a bilateral contract significantly rather than only favoring one side of the agreement to the detriment of the other, generally due to negotiations over the terms of the contract when it was originally drafted (even if it is reused by people who don't themselves negotiate its terms).