Overture, approach, advance, tender, bid are words of somewhat indefinite application covering a variety of acts or actions by which one person or party tries to gain the goodwill of another person or party.
Overture implies an attempt to begin a relationship. It may designate a formal proposal intended to open negotiations (as for peace, for a marriage between persons of royal blood, or for a merger of corporations). It is, however, often applied to an act or speech that may be construed as a search for an opening (as for friendship, for reconciliation, or for cooperation).
Approach, often in the plural, may be used in place of overture when the latter is felt to be too formal.
Advance, usually in the plural, may be applied to an attempt to gain love, friendship, or goodwill, whether it serve as an overture or as an effort to establish a closer relationship and it is the one of these terms that is freely used without qualification to suggest irregularity or impropriety in the overtures made.
Tender retains its primary meaning of offer, but it does not necessarily imply specific acts or a formal proposal. Sometimes it suggests little more than a sign or token.
Bid adds to advance the implication of appeal or, sometimes, of invitation; it always requires qualification. Like the other words of this group, the specific nature of the act or action can be inferred only from the context.