Can someone please explain...

One of the key differences is whether we should work towards equality of opportunity within the current social structures (liberal feminism) or recognise that existing social structures are built round the idea that men's lives are the norm, and women should only be able to participate fully in the public sphere by behaving like men, i.e. pretending that they don't bear and rear children - and argue from that that it is only possible to gain true equality if we reorganise social structures completely.

For example, it is difficult for working mothers to get ahead in a workplace with a culture of presenteeism, and also, often family units do the sums in a straightforward "wife earns X, childcare costs X+d, therefore it is obviously more cost effective for the wife to give up work and become a SAHM." A liberal feminist might look at this situation and say "the solution is to campaign for workplace creches", a radical feminist might look at this situation and say "we need to value properly the enormous and invisible amount of unpaid work women do in the economy, then you see the hidden assumptions not taken into account in the X+d>X calculation." (Note that this latter solution doesn't immediately reach for the conclusion that finding strategies for women to be in the workplace is the right one - it places equal value on SAHM, instead insisting that their unseen economic contribution be valued properly.)

I have a number of friends who talk of "being radicalised by motherhood" - it is relatively easy to think liberal feminism will supply all the answers if you are a young, white, middle class career woman. It becomes much harder as a mother, carer, older, ethnic minority woman.

BTW, I would argue that I'm a radical feminist given the definition above. Trending towards a radical lesbian.

I'd never identify as anything -- academic training, what is the definition of X, and then what evidence do you have for your statement that something is X? Which is why poor ole Pluto (not the dog!), has been demoted to the status of a dwarf planet (and nothing to do with conifers, honest! ).

Feminism and radical feminism aren't the same thing. And 'radical' here doesn't mean 'extreme' or 'violent' or other things that people sometimes seem to think it means.

For me, I understand it as radical meaning 'at the root'. That patriarchal structures have been around since (probably) the agricultural revolution (when we stopped being hunter-gatherers), if not earlier. Hence all existing social structures have developed in that context. For the past six thousand years, as a conservative estimate.

Which would be all nice and interesting historically, except the issue then arises of what you think we need to do (if anything) to improve matters for women. (If you think we need to do something, then that probably makes you a feminist in the loosest sense of the term (i.e. agreeing that women are human beings and deserve equal rights and opportunities to men.)). Whether all we need to do is stick in some legislation and keep telling men to be nice and share, or whether all social structures need to re-imagined and re-created.

Actually, the Wikipedia pages on radical feminism and liberal feminism are quite good!

As far as I can see everyone who identifies as feminist is actually a radical feminist (perhaps I'm wrong though).

You got that the wrong way round - though on mumsnet, there may be some radfems around, the vast majority of women who call themselves feminists are liberal feminists.

Or has feminism become watered down at some point so that everyone now has to call them self a radfem, and 'feminist' has almost become a redundant term.

This is also true. So-called liberal feminism tends to consider all choices a woman makes feminist because a woman makes them. And believe that men can be women, and that there's such a thing as a female penis.
Many women feel that that's not real feminism.

Some women who just do regular mainstream feminism (or what used to be regular feminism) are now branded radical feminists by their opponents.

Or is there no real official definition for either, and it's up to each individual to decide what to identify themselves as?

That, too. Makes it all very complicated because some people nowadays think it's cool to call themselves feminist, but don't actually hold many, or any, feminist opinions.

One uses common sense and reason, the other doesn't.