I can add that the basic difference is in the assumptions of the models. Fixed effects models assume that the effect sizes are all estimates of a single true effect size and that the variance between effect sizes is attributable to sampling error only. Random effects models assume that effect sizes are estimates of their own true effect sizes, distributed around a average true effect, where variance is attributable to both sampling error and 'real' between study variance. Note that if there is only sampling error, the random effects model automatically converges to the fixed effects model. 

The default for which model to choose depends on the field. In medicine people tend to use FE, in social science RE, due to the underlying nature (and possible importance) of the phenomena.

The go-to resource for these questions is probably Borenstein et al., 2009. 

Article An Introduction to Meta-Analysis

Random effects model takes into account the differences between individual study effects, i.e. if the effects across the studies are heterogeneous, then you should use random effects model as it includes between-study random term within the model.  However if the effects across the studies do not differ much, then use fixed effect model.

Random effect estimates can be generalized as it assumes that the studies are just a sample from a population of studies, while if you use fixed effects model, then the estimates is specific to the data that you use.  However, when appropriately used, the fixed effects will give better precision.

Thank you Nik Ruzni Nik Idris for you wonderful interpretation. 

I can add that the basic difference is in the assumptions of the models. Fixed effects models assume that the effect sizes are all estimates of a single true effect size and that the variance between effect sizes is attributable to sampling error only. Random effects models assume that effect sizes are estimates of their own true effect sizes, distributed around a average true effect, where variance is attributable to both sampling error and 'real' between study variance. Note that if there is only sampling error, the random effects model automatically converges to the fixed effects model. 

The default for which model to choose depends on the field. In medicine people tend to use FE, in social science RE, due to the underlying nature (and possible importance) of the phenomena.

The go-to resource for these questions is probably Borenstein et al., 2009. 

Article An Introduction to Meta-Analysis

Thank Robert, adding new idea regarding two model. It is really informative and thanks for sharing an article to clear about these model.

I am not so sure Nik that we can interpret random effects as assuming that the studies are just a sample from a population of studies because in a meta-analysis, the studies are the WHOLE population, so this assumption is usually invalid in practice. I have linked to MetaXL below and the userguide has some interesting information about this

www.epigear.com

Thank you Suhail

I find this paper very helpful when teaching students about fixed effect vs. random effects models in meta-analysis.  It's by the same author as the textbook that Robert mentioned above.  Best of luck!

Thank you Jason

HiI want to know is there difference between fixed effects and fixed effect model. Because I have read some artical they have use OLS or PPML but computed fixed effects of some varibles?

See this discussion:

https://www.researchgate.net/post/Comment_on_Serghiou_S_Goodman_SN_Random-Effects_Meta-analysis_Summarizing_Evidence_With_Caveats_JAMA_2019_3213301-302

Thanks Doi