There is normally no difference. X-like is simply an abbreviated way to say like the/an X, and is often preferred because it is less wordy.
She habitually wore an expression like a cat, of self-satisfied complacency.
She habitually wore a catlike expression of self-satisfied complacency.
She processed the forms with an efficiency like a machine, working through the entire stack in less than an hour.
She processed the forms with machine-like efficiency, working through the entire stack in less than an hour.
Note the construction "X-like" can be used with nearly anything:
He pitched his plan to the group of investors with Trump-like bravado.
(Edit) As stangdon's comment mentions, be careful of confusing the different meanings of "like". For example:
They like a good movie.
is different from
They are like a good movie.
The comment references a popular English grammar pun:
Time flies like an arrow; fruit flies like a banana.
The second part can be interpreted two ways, either "fruit flies (the insect) like bananas" or "fruit flies (through the air) like a banana".
(Edit 2) Lambie's objection is that while flu-like symptoms is fine, symptoms like a/the flu is not. Strictly speaking, I agree. "The flu" is an illness, and is not directly comparable to the symptoms of an illness.
The correct expression should be something like:
symptoms like those that you get from the flu
That being said, many English speakers will shorten this to symptoms like the flu.