Under my umbrella ella ella...

I was just skype-ing with my friend in Notts, when she brought up how she was amused to no end by how the British refer to the umbrella as 'brolly'. Perhaps this is because us, Singaporeans are not lexically primed to use the word 'brolly' to refer to the device which provides us with shelter from the rain and sun. Yet, I was not unable to recognize the term, and so I wondered if it may be used by a select group of Singaporeans as well. Also, it made me wonder about the various other terms used to refer to the same device, like 'parasol'. I decided to conduct a miniature analysis of the terms through looking at the dictionaries at hand.
Brolly

OED:
colloq.

1. Clipped and altered form of

UMBRELLA 2. Term used at both Oxford and Cambridge Universities.

2. slang. A parachute. Also attrib. and Comb., as brolly-hop, a jump made with a parachute; so brolly-hopping vbl. n.

Merriam-Webster:

Main Entry: brol·ly

Pronunciation: \ˈbrä-lē\

Function: noun

Inflected Form(s): plural brollies

Etymology: by shortening & alteration

Date: circa 1874

chiefly British : umbrella

As can be seen by the above lexical entries, it is quite unanimously primed for Br English speakers and is used informally.

Now for the term, 'parasol', which is also seen to be used to refer to the same device, but not quite in exactly the same manner. There is no entire overlap in meaning. My findings are below:

Parasol

OED:

1. Something that screens or protects as if from the rays of the sun.

2. Something that gives shade from the rays of the sun; spec. a screen or canopy, usually in the form of a small light umbrella, often ornamental or brightly coloured; (hence more generally) a sunshade, sun-umbrella.

Merriam-Webster:

Main Entry: par·a·sol

Pronunciation: \ˈper-ə-ˌsȯl, -ˌsäl, ˈpa-rə-\

Function: noun

Etymology: French, from Old Italian parasole, from parare to shield + sole sun, from Latin sol — more at parapet, solar

Date: 1660

: a lightweight umbrella used as a sunshade

Macmillan:

a type of umbrella designed to provide protection from the sun

Oxford Learner's:

para•sol /prsl; NAmE sl; sl/ noun
1 a type of light umbrella that women in the past carried to protect themselves from the sun
2 a large umbrella that is used for example on beaches or outside restaurants to protect people from hot sun—compare sunshade

As can be seen, the term parasol is usually used to refer to a sun shade, and hardly ever for the device used to shelter from rain, which is where the chief distinction lies, across most varieties of English.