I would call it a question of graduations.
The differences are not very apparent when one compares the summarized campaign platforms of the Social Democrats and the Greens. In the long form of the SPD and Green platforms, emphasis becomes clearer, but I believe the key is in what they would trade away in coalition talks. If the election result suggests a coalition containing the SPD and the Greens, there will be plenty of hard bargaining but no insurmountable problems between those two. (They would likely need a third partner, and there the real fault lines will appear.) It would be bad negotiation strategy to highlight "negotiable" and "non-negotiable" parts of the platform in advance ...
- Who pays the price of necessary ecological measures?
Everyone but a fool recognizes that painful changes will be required to mitigate the even more painful consequences of climate change. But who bears the price?
Arguably the Greens are making policies for a sector of society who can afford regional, organic food, and blame those who can only afford industrial food from discount supermarkets. (Not quite the thing called food deserts in the US, but along the same lines.) The Social Democrats, meanwhile, postpone necessary climate action where that would hurt industrial workers e.g. in the coal industry.
And a cynic might say that both parties are in favor of wind power, but the Greens are against wind parks where people or animals live and against high-voltage lines where anyone can see them. The SPD is less likely to block nationally climate-positive infrastructure for their impact on the local scenery.
In much of Germany there is a lack of affordable housing. In many places, the Social Democrats are in favor of building tenement blocks on the last green spaces in a city, while the Greens want to preserve them.
- Policing and Civil Liberty
The police is mostly a matter for the Federal states in Germany, but there is a national framework of laws and agencies. The Greens are more resistant than the Social Democrats to intrusive surveillance and more likely to fight against perceived racial profiling. The Social Democrats are more likely to back higher police budgets.
- The role of the military in foreign policy
There is no national consensus on Bundeswehr missions beyond the NATO area. The Greens are more resistant to such missions, the Social Democrats less so. That's not an absolute -- Foreign Minister Fischer convinced the Greens to back the Balkans missions two decades ago, and enough Social Democrats would rather spend the budget elsewhere.
The biggest difference is the history of both parties which explains a lot of the different priorities and policy settings.
The SPD, being a direct descendent of late-19th century Marxism tends to put social security, workers' rights and similar issues first. On the other hand, large parts of the Green party derive from the ecological movement of the 1970's, so they tend to prioritise nature conservation, a 'natural' lifestyle and ecology.
The areas where these differences are most visible are those where these two ideological backgrounds are in direct opposition. A couple of examples:
Coal and steel. Historically, these industries have employed large workforces and they form(ed?) a significant backbone for the SPD. Thus, the SPD would advocate protecting the coal industry (they were leading figures in establishing coal subsidies when German coal became less competitive due to globalisation). On the other hand, these industries are environmentally very destructive so many in the Green party would fight them to their teeth.
Transport politics. Both parties agree that public transport is a good thing™ but they differ in their principal line of reasoning: for the Greens, it is because public transport is more resource efficient while for the SPD is a cost-effective way for less affluent workers to get from A to B. The difference is clearer when it comes to individual means of transport. In the eyes of the SPD, a worker reaching middle class, being able to afford their own car and then use it efficiently and effectively as an important goal (social mobility). Thus, the SPD tends to be more friendly towards private car use and advocates the appropriate infrastructure (roads/motorways). The Greens on the other hand want to strongly discourage private car ownership – even when it is electrically powered – as they focus primarily on the effects roads, motorways and a car-friendly infrastructure has on the environment and non-car owners. Obviously, fossil fuel powered cars were no-gos for the Greens but even in an era of carbon dioxide-free mobility their arguments against car-friendly road planning would stay relevant.
The difference was even more notable when it came to aviation where the SPD was strongly in favour of increasing access to cheap tickets while the Greens always wanted to reduce aviation as much as possible.
Agriculture. The SPD tends to prioritise cheap and affordable foods. They are not really a party traditionally catering to farmers in any meaningful manner, but the price of bread and milk is very important for their policy considerations. The Greens focus a lot on the environmental impact of agriculture, especially 'conventional' agriculture which relies heavily on the use of fertilisers and pesticides. They instead promote organic farming, arguing that even though bread and milk may become more expensive, the outcome at the end is more positive for everybody.
It may be worth mentioning that the Greens enjoy strong support among farmers of small farms and organic farmers but are often strongly disliked by conventional farmers.
In my hometown, a new bypass was built about 10 years ago and the local council has been considering designating a new industrial zone on what is currently farmland in proximity to the bypass. It should come as no surprise to you after reading the above that the loal SPD was in favour of both while the Greens were against both.
There are certainly more areas where the political ideologies of the two collide.
Disclaimer: I am a member of one of these two parties. I apologise if this has led my post to lack neutrality.