Seeing, as from comments you are interested in any time difference, this is a fairly simple question of vaccine prime and boost strategies.
After an immunization or infection, the adaptive immune system takes some time to be fully activated. This typically involves a primary antibody response that rises over about 20 days and then wanes, and if followed by a secondary exposure to the antigen, rises again to a higher level and then produces a sustained response of varying length, of anything from ~6 months to many years. I'm not an immunologist, but I don't think it is known why some antigens produce a longer humoral response than others.
The immune response follows the pattern seen in the following graph (from Wikimedia Commons):
Image credit: סתו כסלו, CC BY-SA 4.0 https://creativecommons.org/licenses/by-sa/4.0, via Wikimedia Commons
This response is no different for SARS-CoV-2 vaccines than it is for any antigen. Obviously boosting too soon after priming might result in a weaker full response (it might be seen by the body as a single infection), but how soon this might be I don't know and it may not have been studied. I can tell you from having done vaccine research in the past that boosting is rarely less than 20 days post-prime and never shorter than 18 days in my experience.
Most papers that I could find, looked at prime-boost schedules from 4 weeks (28 days) up to much longer (6 months). I found a good paper by Shaw et al.1, from Lancet Respiratory Medicine looking at homologous and heterologous prime-boost using ChAdOx1 and BNT162b2 vaccines at 4 and 12 weeks. Their findings in Figure 1 of the paper show that 12 week booster gives greater anti-spike IgG and neutralizing antibody responses up to 6 months post-vaccination, than a 4 week booster, but that the 4 week booster had a greater cellular (PBMC) response up to 6 months post vaccination.
This implies that primarily a longer, at least up to 12 weeks, separation between prime and boost gives a stronger protection for longer (though add in the risk of infection in that time-space??), and that there is still a strong vaccine protection out to at least 6 mo.
These results seem pretty typical of what I have also found in other papers.
Ref:
- Shaw RH, Liu X, Stuart ASV, Greenland M, Aley PK, Andrews NJ, Cameron JC, Charlton S, Clutterbuck EA, Collins AM, Dejnirattisai W, Dinesh T, Faust SN, Ferreira DM, Finn A, Green CA, Hallis B, Heath PT, Hill H, Lambe T, Lazarus R, Libri V, Long F, Mujadidi YF, Plested EL, Morey ER, Provstgaard-Morys S, Ramasamy MN, Ramsay M, Read RC, Robinson H, Screaton GR, Singh N, Turner DPJ, Turner PJ, Vichos I, Walker LL, White R, Nguyen-Van-Tam JS, Snape MD; Com-COV Study Group. Effect of priming interval on reactogenicity, peak immunological response, and waning after homologous and heterologous COVID-19 vaccine schedules: exploratory analyses of Com-COV, a randomised control trial. Lancet Respir Med. 2022 Nov;10(11):1049-1060. doi: https://doi.org/10.1016/S2213-2600(22)00163-1. Epub 2022 Jun 9. PMID: 35690076; PMCID: PMC9179150.