Direct similarity vs tentative impression
像 states a real resemblance between two things: A像B means A genuinely looks or behaves like B. 他像他妈妈 (he looks like his mother), 这个玩具像小狗 (this toy looks like a puppy). 好像 adds uncertainty: A好像B means A seems like B, based on impression. 他好像他妈妈 would imply "he seems to be like his mother, I am guessing". For factual comparison use 像; for hedge or guess use 好像.
这条鱼像真的一样,但它只是好像在游泳。
Zhè tiáo yú xiàng zhēn de yīyàng, dàn tā zhǐshì hǎoxiàng zài yóuyǒng.
This fish looks real, but it only seems to be swimming.
像 as comparison verb
像 is a full verb: 他像他爸爸 (he resembles his father). It takes a subject and object directly. Negated: 他不像他爸爸 (he does not resemble his father). You can add 很像 for "very much like" or 一点也不像 for "not at all like". In question form: 像不像 (does it look like or not?).
好像 as evidential adverb
好像 is an adverb that modifies the following verb or adjective, adding "seems / looks like". 他好像生病了 (he seems to be sick). It is a softener that lets the speaker avoid a strong assertion. Contrast with 像, which is stronger: 他像生病的人 would mean "he is like a sick person", asserting the similarity. 好像 hedges; 像 asserts.
他好像有点不高兴,我去问问他。
Tā hǎoxiàng yǒudiǎn bù gāoxìng, wǒ qù wènwen tā.
He seems a bit unhappy; I will go ask him.
The 像...一样 structure
像...一样 means "just like, the same as": 像云一样 (like clouds), 像我一样 (like me). This is the Chinese simile construction. The 一样 closes the comparison and adds "the same way". 像他一样聪明 (as smart as him), 像水一样清澈 (as clear as water). 好像 does not use this structure; 好像 stands alone.
他像他哥哥一样爱运动。
Tā xiàng tā gēge yīyàng ài yùndòng.
He loves sports just like his older brother.
好像 in the haoxiang-vs-kanqilai comparison
A separate grammar comparison (haoxiang-vs-kanqilai) covers the difference between 好像 (internal impression) and 看起来 (visual evidence). Here the focus is the 像 vs 好像 split: fact vs impression, verb of comparison vs adverb of tentativeness. The two comparisons reinforce each other; 好像 sits at the intersection of similarity (from 像) and hedging (from its 好 prefix).