Fairly simple. Race is a social construct based on heritage, often groupings of various ethnicities - stuff we literally just made up, usually based things like skin pigments and location of population. Gender is a construct based on sexual identity - which while a social construct in itself, has a basis with inherent biological urges. A transgendered woman won’t share the same biological urges as a man. In other words, they’re two very different things with two different sets of rules defined by culture and politics. 

Both can be changed, though (although transgendered people might feel they’ve always felt different a different gender than their biology would otherwise dictate). Changing either depends on the culture you live in and their own nuances.

You can change your race, it is often a matter of moving to a different culture where the rules for race are different. And you normally won’t have a choice as to what race people think you are in most cases - sometimes there are overlapping definitions, so Jewish people can identify as white or Jewish.
Many cultures allow for gender reassignment which allow people to identify as different genders.

The black question in the US is controversial largely because of the heritage shared by black people. Black in the US is associated with African American heritage, which is genetic heritage by American law. This is why you have the white guy who plays Trevor on Fresh Prince being considered black in the US.

To bring up your example, an ethnic Caucasian might be considered white in the US, but in other locations they’re considered middle eastern, Aryan, or Asian. Different cultures, different definitions. Another example is “Aryan” is a term considered white in the 1930s Nazi culture, but I am talking about the Northern Indian term. Speaking of Indian, in the US Indians are their native population, but again, I am talking about the people of the Northern part of the Indian sub-continent.

Different cultures, different rules, different labels.

In the US at least, most people would tie ethnicity closely with genetic heritage. If you'd prefer to substitute the term genetic heritage in my original statement (I was thinking of what the best term would be but couldn't find it), then feel free to do so. That might be a better term to use.

To use Jessica Krug as an example, she made specific claims for instance that her family was from Algeria (most Algerians are Berbers who some would define as black and others white or arab which would make it a good lie to use) when she, in fact, knew they were not. When she said she was black, she did not mean she identified with black culture or grew up around black culture, she meant that her family came from Africa. And this was not a one off situation where her view of blackness was different than others, so she was misunderstood and later clarified. She continually presented herself in a way that was knowingly deceptive.

I'm not sure how things are in Britain (American or British would be considered nationality and not ethnicity here), but in the US, saying "I'm black" without further clarification would imply that you can trace your ancestry back to Africa in the fairly recent past (like within the past 1000 years or so I dunno the exact cutoff). And we can determine that with a pretty good degree of accuracy.

Transgenderism is also a hormonal thing so it holds some more ground, transracialism is more leaning towards mental disfigurement or social acceptance/pressure/ignorance.
Overall most people have no grasp of what the mind is capable of.

That's what my psychiatrist said after saying she couldn't help me.

Berbers (who make up most of Algeria) have genetic traits that are a mixture of sub-Saharan Africa and Arab. Whether they're black or not is debatable, which is clearly why Krug chose that country. If she'd said Nigeria, people would be like gtfo. 

This is all kind of besides the point. Krug did not misinterpret anything. If she was legitimately from Algeria and considered herself black but others disagreed, that would be a different question entirely. But that's not what happened. She made statements that she knew were objectively not true. Her family was simply not from Algeria, and she knew that they weren't. She was making statements of fact that she knew to be false.

If a trans person was knowingly saying objectively false things, I'd also be against that. If Caitlyn Jenner said she was born with a vagina, then she is lying, and I'd have an issue with that (in the abstract at least... not like I'd go on a vendetta or anything). When Caitlyn Jenner says she feels like she is a woman, I believe she truly believes that. Even if I do feel differently, I defer to her judgment, because she has access to better information than I do. On a sidenote though, fuck Caitlyn Jenner. Not because she's trans, but because she's a shitty person.

The last conversation with my psychiatrist was making an action plan for if I wanted to hurt myself. Due to some insurance issues I didn't make an appointment for the next few months. Never checked in at all. True story.  

Are you feeling better now?

Yeah, thanks for asking. Probably shouldn't have said anything though since it's off topic. 

If transgenderism exists(which it doesn't) then transracialism should also exist. They both revolve around a person adopting a bunch of arbitrary and artificial traits and then demand others to treat them differently because of their misguided beliefs. If black people don't want white people to assume a black identity maybe they shouldn't have crafted an identity out of a skin color. Just like the rest of the world made an identity out of a sex chromosome.

People are fucking crazy. Every day I learn anew how futile it is to fight against religious ignorance just for some assholes to create brand new religions out of thin air. People are hurting each other over thoughts and self expression. That's fucking mental.

The US is kind of fucked up. I was scolded by Americans for singing a rap song off of Strictly 4 my N.I.G.G.A.Z. by Tupac Shakur. They told me that because I wasn’t black I couldn’t sing that.

But look at those hypocrites! Telling me I can’t be black because of the colour of my skin. Now who’s the racist!