Biography
A character who is unusually aggressive and domineering in their relationships and/or romantic/sexual advances yet relinquishes all control the moment it comes to actually having sex with their loved one. This "aggression" falls under two broad categories, which can overlap or sharply diverge.
Abrasive Submissive: Strong-willed, boisterous, or flat-out mean most of the time, but meek and passive when it comes to intimacy.
Forward Submissive: The character very openly seeks out sex, but wants others to take charge of them — possibly being secretive about the latter part until the last moment.
This behavior is commonly displayed by "harsh" Tsunderes. Parallels can be drawn between this and a Faux Action Girl. Indeed, women in fiction end up on the receiving end of this trope much more often than men (cf. Men Act, Women Are). The men who have this trait are often portrayed comically, especially if they don't bother looking for a lover who's into it, or consider it an Unmanly Secret. Although in Courtly Love the (lower status) man will invoke this trope as a way of proving his loyalty to the woman.
An extreme variation, dipping deep into Character Derailment, is often found in fanworks (especially H-Doujinshi) starring a canonically dominant and assertive female character, who remains dominant and assertive right up to the point where the faceless male reader stand-in takes off her clothes.
Note that Tropes Are Tools — this one can present an interesting dichotomy in a character to explore for drama and Character Development. It only becomes off-putting when perpetrated in fanworks upon characters who you'd reasonably expect to behave in bed the same way they do in canon.
For the male/male case, this is a standard (although somewhat less common) type of Uke in Boys' Love Genre works. They're similarly likely to be Tsundere. Because this is a same-sex variation, the Double Standard does not apply, so this trope is generally used in-character. More uncommonly, but still very much present, you will find inversions of this trope, with an aggressive (or even violent) Seme who becomes compliant, gentle and subservient to the Uke's wishes while in-bed — playing with the balance of physical and emotional control in the relationship. The exceptions for in-character usage of this trope are again fanworks where canon characters are used for Wish-Fulfillment.note
Compare Casual Kink, Powerful People Are Subs, Authoritative in Public, Docile in Private, Property of Love, Safe, Sane, and Consensual, and Safe Word. Contrast Naughty by Night.